library(psych)
library(ggplot2)
library(tidyr)
library(car)
library(tidyr)
library(dplyr)
library(corrplot)
library(patchwork)
library(gridExtra)
library(Hmisc)
library(lm.beta)

Load the data

data <- read.csv("/Users/irina/Downloads/MathDTI/DTIMathData.csv")
data <- data[, c("FA_lh_mlf", "FA_rh_mlf", "MD_lh_mlf", "MD_rh_mlf",
                 "RD_lh_mlf", "RD_rh_mlf", "AD_lh_mlf", "AD_rh_mlf",
                 "age","age123",
                 "ADD1", "ADD2", "ADD3", "SUB1", "SUB2", "SUB3",
                 "MUL1", "MUL2", "MUL3", "DIV1", "DIV2", "DIV3",
                 "RT_ADD1", "RT_ADD2", "RT_ADD3",
                 "RT_SUB1" , "RT_SUB2" , "RT_SUB3",
                 "RT_MUL1" , "RT_MUL2", "RT_MUL3",
                 "RT_DIV1", "RT_DIV2", "RT_DIV3")]
#describeBy(data, group='age123')

Plots

Age vs math acc: Scatterplot

# Define the predictor variables and their new names
dependent_vars <- c("ADD1", "ADD2", "ADD3", "SUB1", "SUB2", "SUB3", "MUL1", "MUL2", "MUL3", "DIV1", "DIV2", "DIV3")

#"RT_ADD1", "RT_ADD2", "RT_ADD3", "RT_SUB1", "RT_SUB2", "RT_SUB3", "RT_MUL1", "RT_MUL2", "RT_MUL3", "RT_DIV1", "RT_DIV2", "RT_DIV3")
new_names <- c("Addition Level 1", "Addition Level 2", "Addition Level 3", "Subtraction Level 1", "Subtraction Level 2", "Subtraction Level 3", "Multiplication Level 1", "Multiplication Level 2", "Multiplication Level 3", "Division Level 1", "Division Level 2", "Division Level 3")

# Define colors for each metric
colors <- c("ADD" = "#1f77b4", "SUB" = "#ff7f0e", "MUL" = "#2ca02c", "DIV" = "#d62728")

# Create a list to store plots
plots <- list()

# Create scatterplots with regression lines
for (i in seq_along(dependent_vars)) {
  metric <- substr(dependent_vars[i], 1, 3) # Extract the first three characters of the string stored in dependent_vars
  color <- colors[metric]
  
  
  corr <- cor(data[[dependent_vars[i]]], data$age, use = "complete.obs")
  p_value <- cor.test(data[[dependent_vars[i]]], data$age)$p.value
  
  p <- ggplot(data, aes_string(x = "age", y = dependent_vars[i])) +
    geom_point(color = alpha(color, 0.5), size = 2) +  
    geom_smooth(method = "lm", color = "darkred", size = 0.3, se = FALSE) +  # Dark red and thin regression line
    labs(x = "Age", y = new_names[i]) +
    annotate("text", x = Inf, y = Inf, label = paste0("italic(r) == ", round(corr, 2), " * ',' ~ italic(p) == ",
    format(p_value, digits = 2, scientific = TRUE)), parse = TRUE, hjust = 1.0, vjust = 3) +
    scale_x_continuous(breaks = seq(min(data$age), max(data$age), by = 2)) +
    scale_y_continuous(breaks = seq(0, 1.0, by = 0.2)) +  # Set y-axis limits and step size
    coord_cartesian(ylim = c(0, 1.0)) + 
    theme_minimal() +
    theme(plot.title = element_text(hjust = 0.5), panel.grid = element_blank()) +
    theme(axis.line = element_line(color = "black", size = 0.1))
  
  plots[[i]] <- p
}

# Combine all plots into a single figure
scatterplot_math_age_acc <- wrap_plots(plots, ncol = 3) +
  plot_annotation(title = "Relationships between PMT Accuracy and Age") &
  theme(plot.title = element_text(hjust = 0.5, vjust=1))
#ggsave("scatterplot_math_age_acc.png", scatterplot_math_age_acc, width = 10, height = 8)

# Print the combined plot
print(scatterplot_math_age_acc)
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Age vs math RT: Scatterplot

# Define the predictor variables and their new names
dependent_vars <- c("RT_ADD1", "RT_ADD2", "RT_ADD3", "RT_SUB1", "RT_SUB2", "RT_SUB3", "RT_MUL1", "RT_MUL2", "RT_MUL3", "RT_DIV1", "RT_DIV2", "RT_DIV3")

new_names <- c("Addition Level 1", "Addition Level 2", "Addition Level 3", "Subtraction Level 1", "Subtraction Level 2", "Subtraction Level 3", "Multiplication Level 1", "Multiplication Level 2", "Multiplication Level 3", "Division Level 1", "Division Level 2", "Division Level 3")

# Define colors for each metric
colors <- c("RT_AD" = "#1f77b4", "RT_SU" = "#ff7f0e", "RT_MU" = "#2ca02c", "RT_DI" = "#d62728")

# Create a list to store plots
plots <- list()

# Create scatterplots with regression lines
for (i in seq_along(dependent_vars)) {
  metric <- substr(dependent_vars[i], 1, 5) # Extract the first three characters of the string stored in dependent_vars
  color <- colors[metric]

  corr <- cor(data[[dependent_vars[i]]], data$age, use = "complete.obs")
  p_value <- cor.test(data[[dependent_vars[i]]], data$age)$p.value
  
  p <- ggplot(data, aes_string(x = "age", y = dependent_vars[i])) +
    geom_point(color = alpha(color, 0.5), size = 2) +  
    geom_smooth(method = "lm", color = "darkred", size = 0.3, se = FALSE) +  # Dark red and thin regression line
    labs(x = "Age", y = new_names[i]) +
    annotate("text", x = Inf, y = Inf, label = paste0("italic(r) == ", round(corr, 2), " * ',' ~ italic(p) == ",
    format(p_value, digits = 2, scientific = FALSE)), parse = TRUE, hjust = 1.0, vjust = 1) +
    scale_x_continuous(breaks = seq(min(data$age), max(data$age), by = 2)) +
    scale_y_continuous(breaks = seq(0, 25, by = 5)) +  # Set y-axis limits and step size
    coord_cartesian(ylim = c(0, 20)) + 
    theme_minimal() +
    theme(plot.title = element_text(hjust = 0.5), panel.grid = element_blank()) +
    theme(axis.line = element_line(color = "black", size = 0.1))
  
  plots[[i]] <- p
}

# Combine all plots into a single figure
scatterplot_math_age_rt <- wrap_plots(plots, ncol = 3) +
  plot_annotation(title = "Relationship between PMT Reaction Time and Age") &
  theme(plot.title = element_text(hjust = 0.5, vjust=1))
#ggsave("scatterplot_math_age_rt.png", scatterplot_math_age_rt, width = 10, height = 10)

# Print the combined plot
print(scatterplot_math_age_rt)
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Correlations between DTI metrics

# Define the predictor variables
predictor_vars <- c("FA_lh_mlf", "FA_rh_mlf", "MD_lh_mlf", "MD_rh_mlf", "RD_lh_mlf", "RD_rh_mlf", "AD_lh_mlf", "AD_rh_mlf")

# Calculate the correlation matrix
correlation_matrix <- cor(data[predictor_vars], use = "complete.obs")
colnames(correlation_matrix) <- c("FA left", "FA right", "MD left", "MD right", "RD left", "RD right", "AD left", "AD right")
rownames(correlation_matrix) <- c("FA left", "FA right", "MD left", "MD right", "RD left", "RD right", "AD left", "AD right")

# Define a pastel color palette
pastel_colors <- colorRampPalette(c("#0571B0", "white", "#F8766D"))(200)

# Print the correlation matrix
print(correlation_matrix)
##             FA left   FA right    MD left   MD right    RD left   RD right   AD left  AD right
## FA left   1.0000000  0.6188513 -0.3161599 -0.2742537 -0.6477736 -0.5360513 0.2898058 0.1625369
## FA right  0.6188513  1.0000000 -0.0187502 -0.1183253 -0.2520619 -0.5753438 0.3459605 0.5113776
## MD left  -0.3161599 -0.0187502  1.0000000  0.6388380  0.9253861  0.5302750 0.8122754 0.5426919
## MD right -0.2742537 -0.1183253  0.6388380  1.0000000  0.6296184  0.8775523 0.4597476 0.7885939
## RD left  -0.6477736 -0.2520619  0.9253861  0.6296184  1.0000000  0.6414819 0.5305923 0.3824273
## RD right -0.5360513 -0.5753438  0.5302750  0.8775523  0.6414819  1.0000000 0.1987084 0.3971927
## AD left   0.2898058  0.3459605  0.8122754  0.4597476  0.5305923  0.1987084 1.0000000 0.6251300
## AD right  0.1625369  0.5113776  0.5426919  0.7885939  0.3824273  0.3971927 0.6251300 1.0000000
# Visualize the correlation matrix
corrplot(correlation_matrix, method = "circle", col = pastel_colors, 
         addCoef.col = "black", tl.col = "black", tl.srt = 45, diag=FALSE
         ) #title = "Correlation Matrix"

Correlations between DTI metrics: same plot as above, but exports p-values and Pearson r as a table

# Define the predictor variables
predictor_vars <- c("FA_lh_mlf", "FA_rh_mlf", "MD_lh_mlf", "MD_rh_mlf", "RD_lh_mlf", "RD_rh_mlf", "AD_lh_mlf", "AD_rh_mlf")

# Calculate the correlation matrix and p-values
correlation_results <- rcorr(as.matrix(data[predictor_vars]), type = "pearson")
correlation_matrix <- correlation_results$r
p_values <- correlation_results$P

# Set column and row names
colnames(correlation_matrix) <- c("FA left", "FA right", "MD left", "MD right", "RD left", "RD right", "AD left", "AD right")
rownames(correlation_matrix) <- c("FA left", "FA right", "MD left", "MD right", "RD left", "RD right", "AD left", "AD right")
colnames(p_values) <- colnames(correlation_matrix)
rownames(p_values) <- rownames(correlation_matrix)

# Combine correlation coefficients and p-values into a single data frame
results_table <- data.frame(
  Variable1 = rep(rownames(correlation_matrix), times = ncol(correlation_matrix)),
  Variable2 = rep(colnames(correlation_matrix), each = nrow(correlation_matrix)),
  Correlation = as.vector(correlation_matrix),
  P_Value = as.vector(p_values)
)

# Define a pastel color palette
pastel_colors <- colorRampPalette(c("#0571B0", "white", "#F8766D"))(200)

# Save the plot as a PNG file
png("/Users/irina/Downloads/MathDTI/plots/corr_dti.png", width = 500, height = 500)
#corrplot(correlation_matrix, method = "circle", col = pastel_colors, 
    #     addCoef.col = "black", tl.col = "black", tl.srt = 45, diag=FALSE, tl.cex = 1.5, number.cex = 1.4, alpha=0.5)
#title(main = "Correlations between DTI Metrics", cex.main = 1.4, line = 3, adj = 0.5)

corrplot(correlation_matrix, method = "circle", col = pastel_colors, 
         addCoef.col = "black", tl.col = "black", tl.srt = 45, diag=FALSE,
         tl.cex = 1.5, number.cex = 1.4, font = 1, cl.cex = 1.5)  # Adjust tl.cex, number.cex, font, and cl.cex for larger font size and thinner font
title(main = "Correlations between DTI Metrics", cex.main = 1.7, line = 3, adj = 0.5)

dev.off()
## quartz_off_screen 
##                 3

Standardized model, scaled data

# Define dependent variables
dependent_vars <- c("ADD1", "ADD2", "ADD3", "SUB1", "SUB2", "SUB3", "MUL1", "MUL2", "MUL3", "DIV1", "DIV2", "DIV3",
                    "RT_ADD1", "RT_ADD2", "RT_ADD3", "RT_SUB1", "RT_SUB2", "RT_SUB3", "RT_MUL1", "RT_MUL2",
                    "RT_MUL3", "RT_DIV1", "RT_DIV2", "RT_DIV3")

# List of predictor variable groups
predictor_vars_list <- list(
  c("FA_lh_mlf", "FA_rh_mlf"),
  c("AD_lh_mlf", "AD_rh_mlf"),
  c("RD_lh_mlf", "RD_rh_mlf"),
  c("MD_lh_mlf", "MD_rh_mlf")
)

# Scale the predictor variables
scaled_data <- data
for (predictor_vars in predictor_vars_list) {
  for (var in predictor_vars) {
    scaled_data[[var]] <- scale(data[[var]])
  }
}

# Initialize lists to store the results
lm_results_list <- list()
standardized_results_list <- list()

# Outer loop for different sets of predictor variables
for (predictor_vars in predictor_vars_list) {
  # Loop through each dependent variable
  for (dep_var in dependent_vars) {
    lm_formula <- as.formula(paste(dep_var, "~ age * (", paste(predictor_vars, collapse = " + "), ")"))
    lm_results <- lm(lm_formula, data = scaled_data)
    model_name <- paste(dep_var, paste(predictor_vars, collapse = "_"), sep = "_")
    lm_results_list[[model_name]] <- summary(lm_results)
    
    # Get standardized coefficients
    standardized_model <- lm.beta(lm_results)
    standardized_model_name <- paste(dep_var, paste(predictor_vars, collapse = "_"), "_model_standardized", sep = "_")
    standardized_results_list[[standardized_model_name]] <- summary(standardized_model)
  }
}

# Export lm results
results_df_scaled <- data.frame()
standardized_results_df_scaled <- data.frame()

# Loop through each model in the results list
for (model_name in names(lm_results_list)) {
  summary_model <- lm_results_list[[model_name]]
  coef_df <- as.data.frame(summary_model$coefficients)
  coef_df$Model <- model_name
  results_df_scaled <- rbind(results_df_scaled, coef_df)
}

# Loop through each model in the standardized results list
for (model_name in names(standardized_results_list)) {
  summary_model <- standardized_results_list[[model_name]]
  coef_df <- as.data.frame(summary_model$coefficients)
  coef_df$Model <- model_name
  standardized_results_df_scaled <- rbind(standardized_results_df_scaled, coef_df)
}

# Write results to CSV
#write.csv(results_df_scaled, "lm_results_original_scaled.csv", row.names = TRUE)
#write.csv(standardized_results_df_scaled, "lm_results_standardized_scaled.csv", row.names = TRUE)
#cat("Results have been exported to lm_results_original_scaled.csv and lm_results_standardized_scaled.csv\n")

# Print the summaries of all models
for (model_name in names(lm_results_list)) {
  cat("\nSummary for", model_name, ":\n")
  print(lm_results_list[[model_name]])
}
## 
## Summary for ADD1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.157347 -0.015635  0.006205  0.025858  0.057578 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.8910633  0.0194218  45.879   <2e-16 ***
## age            0.0029732  0.0011509   2.583   0.0128 *  
## FA_lh_mlf     -0.0449507  0.0243582  -1.845   0.0709 .  
## FA_rh_mlf     -0.0013297  0.0255541  -0.052   0.9587    
## age:FA_lh_mlf  0.0029356  0.0015001   1.957   0.0560 .  
## age:FA_rh_mlf -0.0003155  0.0016005  -0.197   0.8445    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04176 on 50 degrees of freedom
## Multiple R-squared:  0.1914, Adjusted R-squared:  0.1105 
## F-statistic: 2.367 on 5 and 50 DF,  p-value: 0.05275
## 
## 
## Summary for ADD2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.29465 -0.06488  0.01612  0.07737  0.20461 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.786157   0.053064  14.815   <2e-16 ***
## age            0.004413   0.003144   1.403    0.167    
## FA_lh_mlf     -0.103441   0.066551  -1.554    0.126    
## FA_rh_mlf     -0.041496   0.069818  -0.594    0.555    
## age:FA_lh_mlf  0.006662   0.004099   1.625    0.110    
## age:FA_rh_mlf  0.001666   0.004373   0.381    0.705    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1141 on 50 degrees of freedom
## Multiple R-squared:  0.1185, Adjusted R-squared:  0.0303 
## F-statistic: 1.344 on 5 and 50 DF,  p-value: 0.2615
## 
## 
## Summary for ADD3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41864 -0.15570  0.02579  0.14116  0.33988 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.639927   0.092482   6.919 8.02e-09 ***
## age            0.006703   0.005480   1.223    0.227    
## FA_lh_mlf      0.119150   0.115988   1.027    0.309    
## FA_rh_mlf     -0.180300   0.121683  -1.482    0.145    
## age:FA_lh_mlf -0.003324   0.007143  -0.465    0.644    
## age:FA_rh_mlf  0.007300   0.007621   0.958    0.343    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1989 on 50 degrees of freedom
## Multiple R-squared:  0.1485, Adjusted R-squared:  0.0634 
## F-statistic: 1.745 on 5 and 50 DF,  p-value: 0.1417
## 
## 
## Summary for SUB1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.113027 -0.023330  0.005069  0.030591  0.088275 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9393790  0.0205105  45.800   <2e-16 ***
## age            0.0006756  0.0012154   0.556    0.581    
## FA_lh_mlf      0.0075278  0.0257235   0.293    0.771    
## FA_rh_mlf     -0.0441038  0.0269865  -1.634    0.108    
## age:FA_lh_mlf -0.0006340  0.0015842  -0.400    0.691    
## age:FA_rh_mlf  0.0021546  0.0016902   1.275    0.208    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0441 on 50 degrees of freedom
## Multiple R-squared:  0.1051, Adjusted R-squared:  0.01564 
## F-statistic: 1.175 on 5 and 50 DF,  p-value: 0.3347
## 
## 
## Summary for SUB2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41473 -0.04313  0.01689  0.06091  0.29791 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.804063   0.061409  13.094   <2e-16 ***
## age            0.002225   0.003639   0.611   0.5437    
## FA_lh_mlf      0.008169   0.077017   0.106   0.9159    
## FA_rh_mlf     -0.144510   0.080798  -1.789   0.0798 .  
## age:FA_lh_mlf  0.001252   0.004743   0.264   0.7928    
## age:FA_rh_mlf  0.006471   0.005060   1.279   0.2069    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.132 on 50 degrees of freedom
## Multiple R-squared:  0.1225, Adjusted R-squared:  0.0348 
## F-statistic: 1.397 on 5 and 50 DF,  p-value: 0.2417
## 
## 
## Summary for SUB3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.62630 -0.17256  0.01021  0.18353  0.45203 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.693050   0.121010   5.727 5.79e-07 ***
## age           -0.002745   0.007171  -0.383   0.7035    
## FA_lh_mlf     -0.054525   0.151766  -0.359   0.7209    
## FA_rh_mlf     -0.289448   0.159217  -1.818   0.0751 .  
## age:FA_lh_mlf  0.006939   0.009347   0.742   0.4613    
## age:FA_rh_mlf  0.015547   0.009972   1.559   0.1253    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2602 on 50 degrees of freedom
## Multiple R-squared:  0.1174, Adjusted R-squared:  0.02914 
## F-statistic:  1.33 on 5 and 50 DF,  p-value: 0.2668
## 
## 
## Summary for MUL1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.151233 -0.023314  0.008036  0.038144  0.074392 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9208457  0.0230348  39.976   <2e-16 ***
## age            0.0021032  0.0013650   1.541    0.130    
## FA_lh_mlf      0.0141810  0.0288894   0.491    0.626    
## FA_rh_mlf     -0.0031023  0.0303078  -0.102    0.919    
## age:FA_lh_mlf -0.0006905  0.0017792  -0.388    0.700    
## age:FA_rh_mlf -0.0006834  0.0018982  -0.360    0.720    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04953 on 50 degrees of freedom
## Multiple R-squared:  0.1076, Adjusted R-squared:  0.01832 
## F-statistic: 1.205 on 5 and 50 DF,  p-value: 0.3204
## 
## 
## Summary for MUL2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.48955 -0.08663  0.00852  0.14219  0.27849 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.6036941  0.0897636   6.725 1.61e-08 ***
## age            0.0109027  0.0053192   2.050   0.0457 *  
## FA_lh_mlf      0.0092279  0.1125782   0.082   0.9350    
## FA_rh_mlf     -0.1346056  0.1181056  -1.140   0.2598    
## age:FA_lh_mlf -0.0004945  0.0069333  -0.071   0.9434    
## age:FA_rh_mlf  0.0067314  0.0073971   0.910   0.3672    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.193 on 50 degrees of freedom
## Multiple R-squared:  0.1139, Adjusted R-squared:  0.02526 
## F-statistic: 1.285 on 5 and 50 DF,  p-value: 0.2852
## 
## 
## Summary for MUL3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.54206 -0.14153 -0.00524  0.18143  0.50304 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    0.183311   0.129026   1.421  0.16160   
## age            0.021964   0.007646   2.873  0.00596 **
## FA_lh_mlf      0.106501   0.161819   0.658  0.51346   
## FA_rh_mlf      0.021119   0.169764   0.124  0.90150   
## age:FA_lh_mlf  0.000179   0.009966   0.018  0.98574   
## age:FA_rh_mlf -0.006697   0.010632  -0.630  0.53164   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2774 on 50 degrees of freedom
## Multiple R-squared:  0.2606, Adjusted R-squared:  0.1866 
## F-statistic: 3.524 on 5 and 50 DF,  p-value: 0.008325
## 
## 
## Summary for DIV1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.31771 -0.02466  0.00914  0.05483  0.19063 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.8468724  0.0457124  18.526   <2e-16 ***
## age            0.0042453  0.0027088   1.567   0.1234    
## FA_lh_mlf      0.0045921  0.0573308   0.080   0.9365    
## FA_rh_mlf     -0.1344924  0.0601457  -2.236   0.0298 *  
## age:FA_lh_mlf -0.0005079  0.0035308  -0.144   0.8862    
## age:FA_rh_mlf  0.0068926  0.0037670   1.830   0.0733 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0983 on 50 degrees of freedom
## Multiple R-squared:  0.1754, Adjusted R-squared:  0.09297 
## F-statistic: 2.127 on 5 and 50 DF,  p-value: 0.07736
## 
## 
## Summary for DIV2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.58961 -0.13072  0.02882  0.18325  0.37085 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.635655   0.113210   5.615 8.63e-07 ***
## age            0.008855   0.006709   1.320    0.193    
## FA_lh_mlf     -0.105032   0.141984  -0.740    0.463    
## FA_rh_mlf     -0.096527   0.148955  -0.648    0.520    
## age:FA_lh_mlf  0.008489   0.008744   0.971    0.336    
## age:FA_rh_mlf  0.003269   0.009329   0.350    0.727    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2434 on 50 degrees of freedom
## Multiple R-squared:  0.089,  Adjusted R-squared:  -0.002101 
## F-statistic: 0.9769 on 5 and 50 DF,  p-value: 0.4411
## 
## 
## Summary for DIV3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.56726 -0.25398  0.05415  0.20112  0.47227 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    0.397038   0.150597   2.636   0.0111 *
## age            0.011882   0.008924   1.331   0.1891  
## FA_lh_mlf     -0.101796   0.188873  -0.539   0.5923  
## FA_rh_mlf      0.166260   0.198146   0.839   0.4054  
## age:FA_lh_mlf  0.008200   0.011632   0.705   0.4841  
## age:FA_rh_mlf -0.012496   0.012410  -1.007   0.3188  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3238 on 50 degrees of freedom
## Multiple R-squared:  0.06289,    Adjusted R-squared:  -0.03082 
## F-statistic: 0.6711 on 5 and 50 DF,  p-value: 0.6472
## 
## 
## Summary for RT_ADD1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8505 -0.3501  0.0438  0.2878  2.3042 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.7168030  0.2505002  10.846 9.76e-15 ***
## age           -0.0623901  0.0148440  -4.203 0.000109 ***
## FA_lh_mlf     -0.0875973  0.3141680  -0.279 0.781531    
## FA_rh_mlf      0.2347075  0.3295930   0.712 0.479705    
## age:FA_lh_mlf -0.0008129  0.0193485  -0.042 0.966657    
## age:FA_rh_mlf -0.0072102  0.0206428  -0.349 0.728344    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5387 on 50 degrees of freedom
## Multiple R-squared:  0.3139, Adjusted R-squared:  0.2453 
## F-statistic: 4.575 on 5 and 50 DF,  p-value: 0.001635
## 
## 
## Summary for RT_ADD2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7671 -1.1161 -0.0237  0.5682  3.8240 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    6.86716    0.72320   9.495 8.91e-13 ***
## age           -0.13234    0.04286  -3.088  0.00328 ** 
## FA_lh_mlf     -1.31341    0.90702  -1.448  0.15384    
## FA_rh_mlf      0.64958    0.95155   0.683  0.49798    
## age:FA_lh_mlf  0.04339    0.05586   0.777  0.44092    
## age:FA_rh_mlf -0.01990    0.05960  -0.334  0.73986    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.555 on 50 degrees of freedom
## Multiple R-squared:  0.2945, Adjusted R-squared:  0.2239 
## F-statistic: 4.174 on 5 and 50 DF,  p-value: 0.00302
## 
## 
## Summary for RT_ADD3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.8186 -1.4216 -0.5410  0.8326  8.1669 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   10.20496    1.33041   7.671 5.39e-10 ***
## age           -0.13977    0.07884  -1.773   0.0823 .  
## FA_lh_mlf     -2.99782    1.66855  -1.797   0.0784 .  
## FA_rh_mlf     -0.35699    1.75047  -0.204   0.8392    
## age:FA_lh_mlf  0.12887    0.10276   1.254   0.2156    
## age:FA_rh_mlf  0.03495    0.10963   0.319   0.7512    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.861 on 50 degrees of freedom
## Multiple R-squared:  0.2079, Adjusted R-squared:  0.1287 
## F-statistic: 2.624 on 5 and 50 DF,  p-value: 0.03491
## 
## 
## Summary for RT_SUB1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.1364 -0.5200 -0.1037  0.2896  8.0782 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.55979    0.63326   5.621 8.43e-07 ***
## age           -0.08695    0.03753  -2.317   0.0246 *  
## FA_lh_mlf      0.04642    0.79421   0.058   0.9536    
## FA_rh_mlf      1.33052    0.83320   1.597   0.1166    
## age:FA_lh_mlf -0.00964    0.04891  -0.197   0.8446    
## age:FA_rh_mlf -0.05831    0.05218  -1.117   0.2692    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.362 on 50 degrees of freedom
## Multiple R-squared:  0.185,  Adjusted R-squared:  0.1035 
## F-statistic:  2.27 on 5 and 50 DF,  p-value: 0.06157
## 
## 
## Summary for RT_SUB2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4549 -1.6739 -0.5684  1.4405  9.4950 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    7.959324   1.137687   6.996 6.09e-09 ***
## age           -0.116549   0.067416  -1.729    0.090 .  
## FA_lh_mlf     -0.470063   1.426845  -0.329    0.743    
## FA_rh_mlf      1.029863   1.496900   0.688    0.495    
## age:FA_lh_mlf  0.001792   0.087874   0.020    0.984    
## age:FA_rh_mlf -0.040673   0.093752  -0.434    0.666    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.446 on 50 degrees of freedom
## Multiple R-squared:  0.1012, Adjusted R-squared:  0.0113 
## F-statistic: 1.126 on 5 and 50 DF,  p-value: 0.359
## 
## 
## Summary for RT_SUB3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.2323  -3.2481  -0.6272   2.4753  14.2244 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    15.5611     2.5074   6.206 1.05e-07 ***
## age            -0.2483     0.1486  -1.671   0.1009    
## FA_lh_mlf      -5.6021     3.1446  -1.781   0.0809 .  
## FA_rh_mlf      -1.5578     3.2990  -0.472   0.6388    
## age:FA_lh_mlf   0.2418     0.1937   1.249   0.2177    
## age:FA_rh_mlf   0.1030     0.2066   0.499   0.6202    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.392 on 50 degrees of freedom
## Multiple R-squared:  0.2172, Adjusted R-squared:  0.139 
## F-statistic: 2.775 on 5 and 50 DF,  p-value: 0.02741
## 
## 
## Summary for RT_MUL1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4574 -0.6408 -0.1239  0.4748  2.8092 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.78211    0.41959   9.014 4.69e-12 ***
## age           -0.09901    0.02486  -3.982 0.000222 ***
## FA_lh_mlf     -0.01276    0.52624  -0.024 0.980758    
## FA_rh_mlf      0.68232    0.55207   1.236 0.222263    
## age:FA_lh_mlf -0.00646    0.03241  -0.199 0.842815    
## age:FA_rh_mlf -0.03155    0.03458  -0.913 0.365864    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9023 on 50 degrees of freedom
## Multiple R-squared:  0.2948, Adjusted R-squared:  0.2243 
## F-statistic:  4.18 on 5 and 50 DF,  p-value: 0.002989
## 
## 
## Summary for RT_MUL2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -5.788 -2.052  0.054  1.206  7.581 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   11.15799    1.43528   7.774 3.72e-10 ***
## age           -0.24141    0.08505  -2.838  0.00654 ** 
## FA_lh_mlf     -3.34712    1.80008  -1.859  0.06886 .  
## FA_rh_mlf      1.73070    1.88846   0.916  0.36383    
## age:FA_lh_mlf  0.12725    0.11086   1.148  0.25649    
## age:FA_rh_mlf -0.06994    0.11828  -0.591  0.55695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.086 on 50 degrees of freedom
## Multiple R-squared:  0.299,  Adjusted R-squared:  0.2289 
## F-statistic: 4.265 on 5 and 50 DF,  p-value: 0.002624
## 
## 
## Summary for RT_MUL3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -12.720  -2.673  -0.688   2.005  14.547 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    19.2424     2.5794   7.460 1.15e-09 ***
## age            -0.3597     0.1529  -2.353   0.0226 *  
## FA_lh_mlf      -5.8570     3.2350  -1.810   0.0762 .  
## FA_rh_mlf      -2.0834     3.3939  -0.614   0.5421    
## age:FA_lh_mlf   0.2320     0.1992   1.164   0.2498    
## age:FA_rh_mlf   0.1769     0.2126   0.832   0.4093    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.547 on 50 degrees of freedom
## Multiple R-squared:  0.2728, Adjusted R-squared:  0.2001 
## F-statistic: 3.751 on 5 and 50 DF,  p-value: 0.005823
## 
## 
## Summary for RT_DIV1_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8978 -0.6983 -0.0363  0.4806  8.8696 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.48411    0.74465   6.022 2.03e-07 ***
## age           -0.12254    0.04413  -2.777   0.0077 ** 
## FA_lh_mlf      0.88881    0.93392   0.952   0.3458    
## FA_rh_mlf      1.34063    0.97977   1.368   0.1773    
## age:FA_lh_mlf -0.05240    0.05752  -0.911   0.3666    
## age:FA_rh_mlf -0.05810    0.06136  -0.947   0.3483    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.601 on 50 degrees of freedom
## Multiple R-squared:  0.2249, Adjusted R-squared:  0.1474 
## F-statistic: 2.901 on 5 and 50 DF,  p-value: 0.02241
## 
## 
## Summary for RT_DIV2_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.5972 -2.3927 -0.4251  1.0468 12.0751 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   12.18886    1.88099   6.480 3.91e-08 ***
## age           -0.24535    0.11146  -2.201   0.0324 *  
## FA_lh_mlf     -2.33658    2.35906  -0.990   0.3267    
## FA_rh_mlf     -1.23445    2.47489  -0.499   0.6201    
## age:FA_lh_mlf  0.05875    0.14529   0.404   0.6877    
## age:FA_rh_mlf  0.10451    0.15500   0.674   0.5033    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.045 on 50 degrees of freedom
## Multiple R-squared:  0.2144, Adjusted R-squared:  0.1358 
## F-statistic: 2.729 on 5 and 50 DF,  p-value: 0.02953
## 
## 
## Summary for RT_DIV3_FA_lh_mlf_FA_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.4693  -3.7415  -0.3158   2.6711  17.3905 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    15.4814     2.7402   5.650 7.63e-07 ***
## age            -0.1864     0.1624  -1.148    0.257    
## FA_lh_mlf       4.3812     3.4367   1.275    0.208    
## FA_rh_mlf      -1.3437     3.6054  -0.373    0.711    
## age:FA_lh_mlf  -0.2311     0.2117  -1.092    0.280    
## age:FA_rh_mlf   0.1063     0.2258   0.471    0.640    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.892 on 50 degrees of freedom
## Multiple R-squared:  0.0632, Adjusted R-squared:  -0.03048 
## F-statistic: 0.6747 on 5 and 50 DF,  p-value: 0.6445
## 
## 
## Summary for ADD1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.176022 -0.017460  0.004908  0.026000  0.061633 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9010815  0.0195696  46.045   <2e-16 ***
## age            0.0025458  0.0011821   2.154   0.0361 *  
## AD_lh_mlf      0.0164281  0.0264715   0.621   0.5377    
## AD_rh_mlf      0.0021655  0.0249790   0.087   0.9313    
## age:AD_lh_mlf -0.0009046  0.0017882  -0.506   0.6152    
## age:AD_rh_mlf -0.0007756  0.0017163  -0.452   0.6533    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0424 on 50 degrees of freedom
## Multiple R-squared:  0.1667, Adjusted R-squared:  0.0834 
## F-statistic: 2.001 on 5 and 50 DF,  p-value: 0.09461
## 
## 
## Summary for ADD2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33652 -0.03951  0.01142  0.06503  0.20017 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.805146   0.053399  15.078   <2e-16 ***
## age            0.003999   0.003226   1.240    0.221    
## AD_lh_mlf      0.026482   0.072232   0.367    0.715    
## AD_rh_mlf     -0.083772   0.068159  -1.229    0.225    
## age:AD_lh_mlf -0.001763   0.004879  -0.361    0.719    
## age:AD_rh_mlf  0.004005   0.004683   0.855    0.396    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1157 on 50 degrees of freedom
## Multiple R-squared:  0.0939, Adjusted R-squared:  0.003287 
## F-statistic: 1.036 on 5 and 50 DF,  p-value: 0.4068
## 
## 
## Summary for ADD3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38728 -0.16528  0.00608  0.15612  0.34369 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.623018   0.090504   6.884 9.12e-09 ***
## age            0.008116   0.005467   1.485   0.1439    
## AD_lh_mlf      0.138292   0.122423   1.130   0.2640    
## AD_rh_mlf     -0.209122   0.115521  -1.810   0.0763 .  
## age:AD_lh_mlf -0.006197   0.008270  -0.749   0.4571    
## age:AD_rh_mlf  0.008896   0.007938   1.121   0.2677    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1961 on 50 degrees of freedom
## Multiple R-squared:  0.1723, Adjusted R-squared:  0.08958 
## F-statistic: 2.082 on 5 and 50 DF,  p-value: 0.08313
## 
## 
## Summary for SUB1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.118058 -0.022622  0.007776  0.032995  0.071786 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9477602  0.0199308  47.553   <2e-16 ***
## age            0.0002269  0.0012039   0.188    0.851    
## AD_lh_mlf      0.0218917  0.0269600   0.812    0.421    
## AD_rh_mlf     -0.0314175  0.0254400  -1.235    0.223    
## age:AD_lh_mlf -0.0016141  0.0018212  -0.886    0.380    
## age:AD_rh_mlf  0.0011914  0.0017480   0.682    0.499    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04318 on 50 degrees of freedom
## Multiple R-squared:  0.1423, Adjusted R-squared:  0.05656 
## F-statistic: 1.659 on 5 and 50 DF,  p-value: 0.1618
## 
## 
## Summary for SUB2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38742 -0.05175  0.00935  0.07371  0.25717 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.828705   0.057071  14.520   <2e-16 ***
## age            0.001120   0.003447   0.325    0.747    
## AD_lh_mlf     -0.020055   0.077200  -0.260    0.796    
## AD_rh_mlf     -0.115915   0.072847  -1.591    0.118    
## age:AD_lh_mlf  0.003292   0.005215   0.631    0.531    
## age:AD_rh_mlf  0.002882   0.005005   0.576    0.567    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1236 on 50 degrees of freedom
## Multiple R-squared:  0.2308, Adjusted R-squared:  0.1538 
## F-statistic:     3 on 5 and 50 DF,  p-value: 0.01914
## 
## 
## Summary for SUB3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.60229 -0.18355  0.01737  0.20608  0.40372 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.708606   0.123674   5.730 5.74e-07 ***
## age           -0.002518   0.007471  -0.337    0.737    
## AD_lh_mlf      0.080033   0.167292   0.478    0.634    
## AD_rh_mlf     -0.126649   0.157860  -0.802    0.426    
## age:AD_lh_mlf -0.001496   0.011301  -0.132    0.895    
## age:AD_rh_mlf  0.002923   0.010847   0.270    0.789    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2679 on 50 degrees of freedom
## Multiple R-squared:  0.06427,    Adjusted R-squared:  -0.02931 
## F-statistic: 0.6868 on 5 and 50 DF,  p-value: 0.6356
## 
## 
## Summary for MUL1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.156168 -0.032025  0.009829  0.033100  0.064797 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.918783   0.023425  39.222   <2e-16 ***
## age            0.002232   0.001415   1.578    0.121    
## AD_lh_mlf      0.016737   0.031687   0.528    0.600    
## AD_rh_mlf     -0.026863   0.029900  -0.898    0.373    
## age:AD_lh_mlf -0.001427   0.002140  -0.667    0.508    
## age:AD_rh_mlf  0.001776   0.002054   0.864    0.391    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05075 on 50 degrees of freedom
## Multiple R-squared:  0.06322,    Adjusted R-squared:  -0.03046 
## F-statistic: 0.6748 on 5 and 50 DF,  p-value: 0.6445
## 
## 
## Summary for MUL2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52272 -0.08951 -0.00284  0.14295  0.27915 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.626640   0.084543   7.412 1.36e-09 ***
## age            0.010051   0.005107   1.968   0.0546 .  
## AD_lh_mlf      0.075915   0.114359   0.664   0.5099    
## AD_rh_mlf     -0.198234   0.107912  -1.837   0.0722 .  
## age:AD_lh_mlf -0.004670   0.007725  -0.604   0.5483    
## age:AD_rh_mlf  0.009063   0.007415   1.222   0.2273    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1832 on 50 degrees of freedom
## Multiple R-squared:  0.2022, Adjusted R-squared:  0.1224 
## F-statistic: 2.534 on 5 and 50 DF,  p-value: 0.04036
## 
## 
## Summary for MUL3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52973 -0.16342 -0.00354  0.16533  0.55713 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    0.112258   0.133441   0.841  0.40421   
## age            0.026142   0.008061   3.243  0.00211 **
## AD_lh_mlf      0.113384   0.180503   0.628  0.53276   
## AD_rh_mlf      0.031601   0.170326   0.186  0.85356   
## age:AD_lh_mlf -0.008035   0.012193  -0.659  0.51291   
## age:AD_rh_mlf -0.001295   0.011703  -0.111  0.91235   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2891 on 50 degrees of freedom
## Multiple R-squared:  0.1972, Adjusted R-squared:  0.1169 
## F-statistic: 2.457 on 5 and 50 DF,  p-value: 0.04569
## 
## 
## Summary for DIV1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.35387 -0.03171  0.01995  0.05953  0.12224 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.854499   0.045258  18.881  < 2e-16 ***
## age            0.004357   0.002734   1.594  0.11729    
## AD_lh_mlf      0.086779   0.061219   1.418  0.16254    
## AD_rh_mlf     -0.158974   0.057768  -2.752  0.00823 ** 
## age:AD_lh_mlf -0.005532   0.004135  -1.338  0.18708    
## age:AD_rh_mlf  0.009174   0.003969   2.311  0.02498 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09805 on 50 degrees of freedom
## Multiple R-squared:  0.1796, Adjusted R-squared:  0.09759 
## F-statistic:  2.19 on 5 and 50 DF,  p-value: 0.07007
## 
## 
## Summary for DIV2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.55256 -0.12697  0.01742  0.16688  0.39112 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.615628   0.104353   5.899 3.13e-07 ***
## age            0.011956   0.006304   1.897   0.0637 .  
## AD_lh_mlf      0.132594   0.141156   0.939   0.3521    
## AD_rh_mlf     -0.386541   0.133197  -2.902   0.0055 ** 
## age:AD_lh_mlf -0.011459   0.009535  -1.202   0.2351    
## age:AD_rh_mlf  0.024264   0.009152   2.651   0.0107 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2261 on 50 degrees of freedom
## Multiple R-squared:  0.2144, Adjusted R-squared:  0.1358 
## F-statistic: 2.729 on 5 and 50 DF,  p-value: 0.02954
## 
## 
## Summary for DIV3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6305 -0.2777  0.0613  0.2467  0.5017 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    0.395490   0.148619   2.661   0.0104 *
## age            0.012168   0.008977   1.355   0.1814  
## AD_lh_mlf     -0.085473   0.201034  -0.425   0.6725  
## AD_rh_mlf      0.025037   0.189699   0.132   0.8955  
## age:AD_lh_mlf  0.001641   0.013580   0.121   0.9043  
## age:AD_rh_mlf -0.001507   0.013034  -0.116   0.9084  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.322 on 50 degrees of freedom
## Multiple R-squared:  0.07365,    Adjusted R-squared:  -0.01899 
## F-statistic: 0.795 on 5 and 50 DF,  p-value: 0.5584
## 
## 
## Summary for RT_ADD1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.82463 -0.33411  0.02597  0.25325  2.32156 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.716634   0.247903  10.958 6.76e-15 ***
## age           -0.063115   0.014975  -4.215 0.000105 ***
## AD_lh_mlf     -0.211254   0.335334  -0.630 0.531575    
## AD_rh_mlf      0.272154   0.316427   0.860 0.393847    
## age:AD_lh_mlf  0.008959   0.022652   0.396 0.694147    
## age:AD_rh_mlf -0.009754   0.021742  -0.449 0.655629    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5371 on 50 degrees of freedom
## Multiple R-squared:  0.318,  Adjusted R-squared:  0.2498 
## F-statistic: 4.662 on 5 and 50 DF,  p-value: 0.001433
## 
## 
## Summary for RT_ADD2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9945 -1.1485 -0.1579  0.5768  3.5128 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    7.1860122  0.7394387   9.718 4.17e-13 ***
## age           -0.1493360  0.0446664  -3.343  0.00157 ** 
## AD_lh_mlf     -0.8446375  1.0002264  -0.844  0.40244    
## AD_rh_mlf      0.3479995  0.9438313   0.369  0.71390    
## age:AD_lh_mlf  0.0295052  0.0675658   0.437  0.66422    
## age:AD_rh_mlf  0.0009735  0.0648519   0.015  0.98808    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.602 on 50 degrees of freedom
## Multiple R-squared:  0.2514, Adjusted R-squared:  0.1765 
## F-statistic: 3.358 on 5 and 50 DF,  p-value: 0.01082
## 
## 
## Summary for RT_ADD3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9808 -1.8458 -0.4902  0.9297  9.6705 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   11.12352    1.38705   8.020 1.55e-10 ***
## age           -0.18176    0.08379  -2.169   0.0348 *  
## AD_lh_mlf     -0.40023    1.87624  -0.213   0.8320    
## AD_rh_mlf     -1.42897    1.77045  -0.807   0.4234    
## age:AD_lh_mlf  0.03460    0.12674   0.273   0.7860    
## age:AD_rh_mlf  0.08577    0.12165   0.705   0.4840    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.005 on 50 degrees of freedom
## Multiple R-squared:  0.1261, Adjusted R-squared:  0.0387 
## F-statistic: 1.443 on 5 and 50 DF,  p-value: 0.2254
## 
## 
## Summary for RT_SUB1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7520 -0.6427 -0.2162  0.3337  8.3339 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.3906403  0.6372341   5.321 2.43e-06 ***
## age           -0.0807715  0.0384927  -2.098   0.0409 *  
## AD_lh_mlf      0.0106113  0.8619758   0.012   0.9902    
## AD_rh_mlf      0.9133311  0.8133756   1.123   0.2668    
## age:AD_lh_mlf  0.0008573  0.0582269   0.015   0.9883    
## age:AD_rh_mlf -0.0391234  0.0558881  -0.700   0.4872    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.38 on 50 degrees of freedom
## Multiple R-squared:  0.1624, Adjusted R-squared:  0.07862 
## F-statistic: 1.939 on 5 and 50 DF,  p-value: 0.1044
## 
## 
## Summary for RT_SUB2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2713 -1.5321 -0.6067  1.0334  9.9493 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    8.141215   1.137128   7.159 3.38e-09 ***
## age           -0.128798   0.068689  -1.875   0.0666 .  
## AD_lh_mlf     -0.897442   1.538174  -0.583   0.5622    
## AD_rh_mlf      0.028579   1.451448   0.020   0.9844    
## age:AD_lh_mlf  0.051904   0.103904   0.500   0.6196    
## age:AD_rh_mlf  0.008145   0.099731   0.082   0.9352    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.463 on 50 degrees of freedom
## Multiple R-squared:  0.08859,    Adjusted R-squared:  -0.002547 
## F-statistic: 0.9721 on 5 and 50 DF,  p-value: 0.444
## 
## 
## Summary for RT_SUB3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.1398  -3.2497  -0.9973   2.4507  12.0327 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   17.70524    2.50021   7.081 4.47e-09 ***
## age           -0.34962    0.15103  -2.315   0.0248 *  
## AD_lh_mlf     -1.47559    3.38199  -0.436   0.6645    
## AD_rh_mlf     -4.50735    3.19131  -1.412   0.1640    
## age:AD_lh_mlf  0.05737    0.22846   0.251   0.8027    
## age:AD_rh_mlf  0.21813    0.21928   0.995   0.3246    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.416 on 50 degrees of freedom
## Multiple R-squared:   0.21,  Adjusted R-squared:  0.131 
## F-statistic: 2.658 on 5 and 50 DF,  p-value: 0.03306
## 
## 
## Summary for RT_MUL1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3029 -0.5607 -0.1714  0.4499  2.3794 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.77287    0.40815   9.244 2.12e-12 ***
## age           -0.10198    0.02465  -4.136 0.000135 ***
## AD_lh_mlf     -0.78584    0.55209  -1.423 0.160834    
## AD_rh_mlf      0.89484    0.52097   1.718 0.092046 .  
## age:AD_lh_mlf  0.04194    0.03729   1.125 0.266108    
## age:AD_rh_mlf -0.04470    0.03580  -1.249 0.217569    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8842 on 50 degrees of freedom
## Multiple R-squared:  0.3227, Adjusted R-squared:  0.255 
## F-statistic: 4.765 on 5 and 50 DF,  p-value: 0.001227
## 
## 
## Summary for RT_MUL2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.7400 -2.1399 -0.6008  0.9545  9.9783 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   12.08021    1.49186   8.097 1.18e-10 ***
## age           -0.29072    0.09012  -3.226  0.00222 ** 
## AD_lh_mlf     -2.18103    2.01801  -1.081  0.28498    
## AD_rh_mlf      0.34790    1.90423   0.183  0.85577    
## age:AD_lh_mlf  0.09813    0.13632   0.720  0.47499    
## age:AD_rh_mlf  0.00574    0.13084   0.044  0.96519    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.232 on 50 degrees of freedom
## Multiple R-squared:  0.2313, Adjusted R-squared:  0.1544 
## F-statistic: 3.008 on 5 and 50 DF,  p-value: 0.01887
## 
## 
## Summary for RT_MUL3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.0314  -3.1461  -0.6497   2.2128  12.9596 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    21.6842     2.6231   8.267 6.45e-11 ***
## age            -0.4799     0.1584  -3.028  0.00388 ** 
## AD_lh_mlf      -2.3536     3.5482  -0.663  0.51017    
## AD_rh_mlf      -4.0357     3.3482  -1.205  0.23374    
## age:AD_lh_mlf   0.1530     0.2397   0.638  0.52614    
## age:AD_rh_mlf   0.1766     0.2301   0.768  0.44634    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.683 on 50 degrees of freedom
## Multiple R-squared:  0.2367, Adjusted R-squared:  0.1603 
## F-statistic: 3.101 on 5 and 50 DF,  p-value: 0.01629
## 
## 
## Summary for RT_DIV1_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0569 -0.8110 -0.1282  0.7121  9.6008 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.09743    0.76103   5.384 1.95e-06 ***
## age           -0.10699    0.04597  -2.327    0.024 *  
## AD_lh_mlf     -0.34662    1.02943  -0.337    0.738    
## AD_rh_mlf      1.23130    0.97139   1.268    0.211    
## age:AD_lh_mlf  0.02248    0.06954   0.323    0.748    
## age:AD_rh_mlf -0.05457    0.06675  -0.818    0.417    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.649 on 50 degrees of freedom
## Multiple R-squared:  0.1783, Adjusted R-squared:  0.09608 
## F-statistic: 2.169 on 5 and 50 DF,  p-value: 0.07238
## 
## 
## Summary for RT_DIV2_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3227 -2.5867 -0.6478  0.8392 14.2697 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   13.28944    1.95346   6.803 1.22e-08 ***
## age           -0.30529    0.11800  -2.587   0.0126 *  
## AD_lh_mlf     -1.48042    2.64241  -0.560   0.5778    
## AD_rh_mlf     -0.07573    2.49343  -0.030   0.9759    
## age:AD_lh_mlf  0.08217    0.17850   0.460   0.6473    
## age:AD_rh_mlf  0.01317    0.17133   0.077   0.9390    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.232 on 50 degrees of freedom
## Multiple R-squared:   0.14,  Adjusted R-squared:  0.05395 
## F-statistic: 1.627 on 5 and 50 DF,  p-value: 0.17
## 
## 
## Summary for RT_DIV3_AD_lh_mlf_AD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.4536  -2.7051  -0.7691   2.4556  17.0550 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    14.3835     2.6378   5.453 1.53e-06 ***
## age            -0.1414     0.1593  -0.887   0.3791    
## AD_lh_mlf      -7.5310     3.5681  -2.111   0.0398 *  
## AD_rh_mlf       3.5314     3.3669   1.049   0.2993    
## age:AD_lh_mlf   0.4219     0.2410   1.751   0.0862 .  
## age:AD_rh_mlf  -0.1691     0.2313  -0.731   0.4683    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.714 on 50 degrees of freedom
## Multiple R-squared:  0.1189, Adjusted R-squared:  0.0308 
## F-statistic:  1.35 on 5 and 50 DF,  p-value: 0.2592
## 
## 
## Summary for ADD1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.182452 -0.020227  0.006315  0.023575  0.058412 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.8917740  0.0196002  45.498   <2e-16 ***
## age            0.0029931  0.0011743   2.549   0.0139 *  
## RD_lh_mlf      0.0424597  0.0237693   1.786   0.0801 .  
## RD_rh_mlf     -0.0063609  0.0269524  -0.236   0.8144    
## age:RD_lh_mlf -0.0027314  0.0014127  -1.933   0.0588 .  
## age:RD_rh_mlf  0.0003832  0.0015321   0.250   0.8035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04163 on 50 degrees of freedom
## Multiple R-squared:  0.1964, Adjusted R-squared:  0.116 
## F-statistic: 2.444 on 5 and 50 DF,  p-value: 0.04662
## 
## 
## Summary for ADD2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36573 -0.05423  0.01482  0.06796  0.15964 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.794863   0.054671  14.539   <2e-16 ***
## age            0.004427   0.003275   1.351    0.183    
## RD_lh_mlf      0.100921   0.066300   1.522    0.134    
## RD_rh_mlf     -0.093326   0.075179  -1.241    0.220    
## age:RD_lh_mlf -0.006056   0.003940  -1.537    0.131    
## age:RD_rh_mlf  0.004767   0.004274   1.115    0.270    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1161 on 50 degrees of freedom
## Multiple R-squared:  0.08688,    Adjusted R-squared:  -0.004435 
## F-statistic: 0.9514 on 5 and 50 DF,  p-value: 0.4564
## 
## 
## Summary for ADD3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.48113 -0.17365  0.04247  0.17703  0.32968 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.618560   0.097804   6.324 6.84e-08 ***
## age            0.008185   0.005860   1.397    0.169    
## RD_lh_mlf      0.018653   0.118608   0.157    0.876    
## RD_rh_mlf     -0.080710   0.134491  -0.600    0.551    
## age:RD_lh_mlf -0.002127   0.007049  -0.302    0.764    
## age:RD_rh_mlf  0.004062   0.007645   0.531    0.598    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2077 on 50 degrees of freedom
## Multiple R-squared:  0.07076,    Adjusted R-squared:  -0.02216 
## F-statistic: 0.7615 on 5 and 50 DF,  p-value: 0.5818
## 
## 
## Summary for SUB1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.14931 -0.02070  0.01064  0.03121  0.05239 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9455473  0.0218632  43.248   <2e-16 ***
## age            0.0002687  0.0013099   0.205    0.838    
## RD_lh_mlf      0.0046829  0.0265137   0.177    0.861    
## RD_rh_mlf      0.0017354  0.0300643   0.058    0.954    
## age:RD_lh_mlf -0.0003516  0.0015758  -0.223    0.824    
## age:RD_rh_mlf -0.0002003  0.0017090  -0.117    0.907    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04644 on 50 degrees of freedom
## Multiple R-squared:  0.007796,   Adjusted R-squared:  -0.09142 
## F-statistic: 0.07857 on 5 and 50 DF,  p-value: 0.9952
## 
## 
## Summary for SUB2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52093 -0.02886  0.03287  0.09272  0.16337 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.8157231  0.0647685  12.594   <2e-16 ***
## age            0.0019845  0.0038804   0.511    0.611    
## RD_lh_mlf      0.0078255  0.0785454   0.100    0.921    
## RD_rh_mlf     -0.0657399  0.0890638  -0.738    0.464    
## age:RD_lh_mlf -0.0005345  0.0046682  -0.115    0.909    
## age:RD_rh_mlf  0.0025608  0.0050628   0.506    0.615    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1376 on 50 degrees of freedom
## Multiple R-squared:  0.04752,    Adjusted R-squared:  -0.04772 
## F-statistic: 0.4989 on 5 and 50 DF,  p-value: 0.7755
## 
## 
## Summary for SUB3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.65838 -0.16586  0.04222  0.19584  0.37584 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.693446   0.127772   5.427 1.67e-06 ***
## age           -0.002406   0.007655  -0.314    0.755    
## RD_lh_mlf      0.083200   0.154951   0.537    0.594    
## RD_rh_mlf      0.033013   0.175701   0.188    0.852    
## age:RD_lh_mlf -0.005898   0.009209  -0.640    0.525    
## age:RD_rh_mlf -0.003402   0.009988  -0.341    0.735    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2714 on 50 degrees of freedom
## Multiple R-squared:  0.0398, Adjusted R-squared:  -0.05622 
## F-statistic: 0.4145 on 5 and 50 DF,  p-value: 0.8365
## 
## 
## Summary for MUL1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.162168 -0.023295  0.006575  0.040165  0.062643 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9147456  0.0235266  38.881   <2e-16 ***
## age            0.0024648  0.0014095   1.749   0.0865 .  
## RD_lh_mlf     -0.0083766  0.0285309  -0.294   0.7703    
## RD_rh_mlf      0.0031898  0.0323516   0.099   0.9219    
## age:RD_lh_mlf  0.0001093  0.0016957   0.064   0.9489    
## age:RD_rh_mlf  0.0006308  0.0018390   0.343   0.7330    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04997 on 50 degrees of freedom
## Multiple R-squared:  0.09157,    Adjusted R-squared:  0.0007253 
## F-statistic: 1.008 on 5 and 50 DF,  p-value: 0.4229
## 
## 
## Summary for MUL2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52561 -0.10166  0.02307  0.12703  0.33579 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.625090   0.090793   6.885 9.09e-09 ***
## age            0.010074   0.005440   1.852   0.0699 .  
## RD_lh_mlf      0.065283   0.110105   0.593   0.5559    
## RD_rh_mlf     -0.151922   0.124850  -1.217   0.2294    
## age:RD_lh_mlf -0.003843   0.006544  -0.587   0.5596    
## age:RD_rh_mlf  0.007219   0.007097   1.017   0.3140    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1929 on 50 degrees of freedom
## Multiple R-squared:  0.1154, Adjusted R-squared:  0.02691 
## F-statistic: 1.304 on 5 and 50 DF,  p-value: 0.2773
## 
## 
## Summary for MUL3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.61108 -0.15658 -0.02475  0.17862  0.47835 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    0.121492   0.130309   0.932  0.35565   
## age            0.025190   0.007807   3.227  0.00221 **
## RD_lh_mlf     -0.087056   0.158027  -0.551  0.58416   
## RD_rh_mlf      0.155069   0.179190   0.865  0.39096   
## age:RD_lh_mlf -0.001602   0.009392  -0.171  0.86525   
## age:RD_rh_mlf -0.003657   0.010186  -0.359  0.72112   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2768 on 50 degrees of freedom
## Multiple R-squared:  0.264,  Adjusted R-squared:  0.1904 
## F-statistic: 3.587 on 5 and 50 DF,  p-value: 0.007532
## 
## 
## Summary for DIV1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40804 -0.01672  0.02967  0.05637  0.10683 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.844845   0.049699  16.999   <2e-16 ***
## age            0.004611   0.002978   1.548    0.128    
## RD_lh_mlf      0.035421   0.060270   0.588    0.559    
## RD_rh_mlf     -0.032255   0.068342  -0.472    0.639    
## age:RD_lh_mlf -0.001806   0.003582  -0.504    0.616    
## age:RD_rh_mlf  0.002240   0.003885   0.577    0.567    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1056 on 50 degrees of freedom
## Multiple R-squared:  0.04891,    Adjusted R-squared:  -0.0462 
## F-statistic: 0.5143 on 5 and 50 DF,  p-value: 0.7642
## 
## 
## Summary for DIV2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53569 -0.12525  0.06988  0.18164  0.35545 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.633217   0.111719   5.668 7.15e-07 ***
## age            0.010400   0.006693   1.554   0.1266    
## RD_lh_mlf      0.162568   0.135483   1.200   0.2358    
## RD_rh_mlf     -0.297554   0.153626  -1.937   0.0584 .  
## age:RD_lh_mlf -0.012082   0.008052  -1.500   0.1398    
## age:RD_rh_mlf  0.017655   0.008733   2.022   0.0486 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2373 on 50 degrees of freedom
## Multiple R-squared:  0.1343, Adjusted R-squared:  0.04773 
## F-statistic: 1.551 on 5 and 50 DF,  p-value: 0.1911
## 
## 
## Summary for DIV3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.60538 -0.22555  0.03192  0.22854  0.51545 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    0.414386   0.151244   2.740   0.0085 **
## age            0.011168   0.009061   1.232   0.2235   
## RD_lh_mlf     -0.049505   0.183415  -0.270   0.7883   
## RD_rh_mlf     -0.008763   0.207977  -0.042   0.9666   
## age:RD_lh_mlf -0.001861   0.010901  -0.171   0.8651   
## age:RD_rh_mlf  0.002901   0.011822   0.245   0.8072   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3213 on 50 degrees of freedom
## Multiple R-squared:  0.07768,    Adjusted R-squared:  -0.01456 
## F-statistic: 0.8422 on 5 and 50 DF,  p-value: 0.5263
## 
## 
## Summary for RT_ADD1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.76793 -0.35428  0.05524  0.28011  2.44032 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.762262   0.257889  10.711 1.52e-14 ***
## age           -0.065538   0.015451  -4.242 9.57e-05 ***
## RD_lh_mlf     -0.086170   0.312745  -0.276    0.784    
## RD_rh_mlf      0.097825   0.354626   0.276    0.784    
## age:RD_lh_mlf  0.007542   0.018587   0.406    0.687    
## age:RD_rh_mlf -0.006729   0.020159  -0.334    0.740    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5478 on 50 degrees of freedom
## Multiple R-squared:  0.2904, Adjusted R-squared:  0.2194 
## F-statistic: 4.092 on 5 and 50 DF,  p-value: 0.003423
## 
## 
## Summary for RT_ADD2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.4784 -1.2143 -0.0481  0.6604  3.6517 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    7.129055   0.765772   9.310 1.69e-12 ***
## age           -0.145228   0.045879  -3.165  0.00264 ** 
## RD_lh_mlf      0.402150   0.928659   0.433  0.66685    
## RD_rh_mlf     -0.245707   1.053021  -0.233  0.81645    
## age:RD_lh_mlf -0.009721   0.055193  -0.176  0.86090    
## age:RD_rh_mlf  0.014977   0.059858   0.250  0.80345    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.627 on 50 degrees of freedom
## Multiple R-squared:  0.2281, Adjusted R-squared:  0.1509 
## F-statistic: 2.955 on 5 and 50 DF,  p-value: 0.02055
## 
## 
## Summary for RT_ADD3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.7087 -1.5550 -0.5678  1.2359  8.3838 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   10.42417    1.36379   7.644 5.94e-10 ***
## age           -0.13915    0.08171  -1.703   0.0948 .  
## RD_lh_mlf      2.47354    1.65389   1.496   0.1410    
## RD_rh_mlf     -2.14805    1.87537  -1.145   0.2575    
## age:RD_lh_mlf -0.08884    0.09830  -0.904   0.3705    
## age:RD_rh_mlf  0.10919    0.10660   1.024   0.3106    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.897 on 50 degrees of freedom
## Multiple R-squared:  0.1878, Adjusted R-squared:  0.1065 
## F-statistic: 2.312 on 5 and 50 DF,  p-value: 0.05763
## 
## 
## Summary for RT_SUB1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2414 -0.4934 -0.2421  0.1962  9.0973 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.485993   0.672721   5.182 3.95e-06 ***
## age           -0.084528   0.040304  -2.097    0.041 *  
## RD_lh_mlf      0.301378   0.815815   0.369    0.713    
## RD_rh_mlf     -0.387092   0.925065  -0.418    0.677    
## age:RD_lh_mlf -0.007279   0.048486  -0.150    0.881    
## age:RD_rh_mlf  0.012318   0.052585   0.234    0.816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.429 on 50 degrees of freedom
## Multiple R-squared:  0.1025, Adjusted R-squared:  0.01279 
## F-statistic: 1.143 on 5 and 50 DF,  p-value: 0.3505
## 
## 
## Summary for RT_SUB2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3839 -1.4275 -0.6823  1.2556  9.5187 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    8.094376   1.150247   7.037 5.25e-09 ***
## age           -0.120442   0.068913  -1.748   0.0867 .  
## RD_lh_mlf      0.460273   1.394915   0.330   0.7428    
## RD_rh_mlf     -1.478704   1.581716  -0.935   0.3543    
## age:RD_lh_mlf -0.004394   0.082904  -0.053   0.9579    
## age:RD_rh_mlf  0.072442   0.089912   0.806   0.4242    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.443 on 50 degrees of freedom
## Multiple R-squared:  0.1035, Adjusted R-squared:  0.0138 
## F-statistic: 1.154 on 5 and 50 DF,  p-value: 0.3449
## 
## 
## Summary for RT_SUB3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.5832  -2.8900  -0.5105   1.6923  13.0722 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    16.9189     2.6257   6.443 4.46e-08 ***
## age            -0.2992     0.1573  -1.902   0.0629 .  
## RD_lh_mlf       4.8832     3.1843   1.534   0.1314    
## RD_rh_mlf      -6.5970     3.6107  -1.827   0.0737 .  
## age:RD_lh_mlf  -0.2177     0.1893  -1.151   0.2554    
## age:RD_rh_mlf   0.3164     0.2052   1.541   0.1295    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.577 on 50 degrees of freedom
## Multiple R-squared:  0.1623, Adjusted R-squared:  0.07857 
## F-statistic: 1.938 on 5 and 50 DF,  p-value: 0.1045
## 
## 
## Summary for RT_MUL1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2819 -0.6127 -0.1099  0.3941  2.5927 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.87616    0.43205   8.972 5.43e-12 ***
## age           -0.10606    0.02588  -4.098 0.000153 ***
## RD_lh_mlf     -0.53329    0.52395  -1.018 0.313662    
## RD_rh_mlf      0.40694    0.59412   0.685 0.496538    
## age:RD_lh_mlf  0.03171    0.03114   1.018 0.313400    
## age:RD_rh_mlf -0.02320    0.03377  -0.687 0.495259    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9177 on 50 degrees of freedom
## Multiple R-squared:  0.2704, Adjusted R-squared:  0.1974 
## F-statistic: 3.706 on 5 and 50 DF,  p-value: 0.006251
## 
## 
## Summary for RT_MUL2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.0745 -2.0771 -0.5475  1.2365 10.6368 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   11.83526    1.53225   7.724 4.45e-10 ***
## age           -0.27122    0.09180  -2.954  0.00477 ** 
## RD_lh_mlf      1.18124    1.85818   0.636  0.52787    
## RD_rh_mlf     -1.53194    2.10702  -0.727  0.47057    
## age:RD_lh_mlf -0.02852    0.11044  -0.258  0.79725    
## age:RD_rh_mlf  0.07659    0.11977   0.639  0.52544    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.255 on 50 degrees of freedom
## Multiple R-squared:  0.2204, Adjusted R-squared:  0.1424 
## F-statistic: 2.827 on 5 and 50 DF,  p-value: 0.02523
## 
## 
## Summary for RT_MUL3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.337  -2.616  -0.448   2.961  12.823 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    20.8135     2.6831   7.757 3.95e-10 ***
## age            -0.4223     0.1607  -2.627   0.0114 *  
## RD_lh_mlf       4.7201     3.2538   1.451   0.1531    
## RD_rh_mlf      -6.3761     3.6895  -1.728   0.0901 .  
## age:RD_lh_mlf  -0.1644     0.1934  -0.850   0.3992    
## age:RD_rh_mlf   0.2701     0.2097   1.288   0.2038    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.699 on 50 degrees of freedom
## Multiple R-squared:  0.2322, Adjusted R-squared:  0.1554 
## F-statistic: 3.024 on 5 and 50 DF,  p-value: 0.0184
## 
## 
## Summary for RT_DIV1_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5500 -0.8730 -0.2300  0.4543 10.5142 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.38629    0.80329   5.460 1.49e-06 ***
## age           -0.12084    0.04813  -2.511   0.0153 *  
## RD_lh_mlf     -0.59904    0.97415  -0.615   0.5414    
## RD_rh_mlf      0.06441    1.10461   0.058   0.9537    
## age:RD_lh_mlf  0.03732    0.05790   0.645   0.5221    
## age:RD_rh_mlf -0.01116    0.06279  -0.178   0.8597    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.706 on 50 degrees of freedom
## Multiple R-squared:  0.1198, Adjusted R-squared:  0.03179 
## F-statistic: 1.361 on 5 and 50 DF,  p-value: 0.2548
## 
## 
## Summary for RT_DIV2_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.0688 -2.2054 -0.6775  1.6506 11.5302 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   12.728121   1.956580   6.505 3.57e-08 ***
## age           -0.272891   0.117222  -2.328    0.024 *  
## RD_lh_mlf      0.783451   2.372761   0.330    0.743    
## RD_rh_mlf      0.496095   2.690511   0.184    0.854    
## age:RD_lh_mlf  0.007855   0.141020   0.056    0.956    
## age:RD_rh_mlf -0.032492   0.152941  -0.212    0.833    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.156 on 50 degrees of freedom
## Multiple R-squared:  0.1705, Adjusted R-squared:  0.08758 
## F-statistic: 2.056 on 5 and 50 DF,  p-value: 0.08672
## 
## 
## Summary for RT_DIV3_RD_lh_mlf_RD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.7807  -3.4483  -0.4494   3.6501  15.9075 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    16.3133     2.5922   6.293 7.65e-08 ***
## age            -0.2445     0.1553  -1.574  0.12175    
## RD_lh_mlf      -9.3441     3.1436  -2.972  0.00453 ** 
## RD_rh_mlf       5.5791     3.5646   1.565  0.12385    
## age:RD_lh_mlf   0.4758     0.1868   2.547  0.01400 *  
## age:RD_rh_mlf  -0.3024     0.2026  -1.492  0.14193    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.506 on 50 degrees of freedom
## Multiple R-squared:  0.182,  Adjusted R-squared:  0.1002 
## F-statistic: 2.224 on 5 and 50 DF,  p-value: 0.06628
## 
## 
## Summary for ADD1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.183883 -0.016291  0.007712  0.025404  0.052865 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.8961162  0.0195627  45.807   <2e-16 ***
## age            0.0027985  0.0011756   2.380   0.0211 *  
## MD_lh_mlf      0.0399122  0.0238191   1.676   0.1001    
## MD_rh_mlf     -0.0118426  0.0243370  -0.487   0.6287    
## age:MD_lh_mlf -0.0025048  0.0014747  -1.699   0.0956 .  
## age:MD_rh_mlf  0.0004261  0.0014591   0.292   0.7715    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04181 on 50 degrees of freedom
## Multiple R-squared:  0.1895, Adjusted R-squared:  0.1085 
## F-statistic: 2.338 on 5 and 50 DF,  p-value: 0.05523
## 
## 
## Summary for ADD2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33854 -0.03909  0.00807  0.06447  0.18251 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.802791   0.053694  14.951   <2e-16 ***
## age            0.004133   0.003227   1.281   0.2062    
## MD_lh_mlf      0.093459   0.065377   1.430   0.1591    
## MD_rh_mlf     -0.112999   0.066798  -1.692   0.0969 .  
## age:MD_lh_mlf -0.005631   0.004048  -1.391   0.1703    
## age:MD_rh_mlf  0.005567   0.004005   1.390   0.1707    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1148 on 50 degrees of freedom
## Multiple R-squared:  0.1083, Adjusted R-squared:  0.01909 
## F-statistic: 1.214 on 5 and 50 DF,  p-value: 0.3163
## 
## 
## Summary for ADD3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.43572 -0.17334  0.03414  0.16940  0.33702 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.617826   0.094415   6.544 3.11e-08 ***
## age            0.008459   0.005674   1.491   0.1423    
## MD_lh_mlf      0.111132   0.114957   0.967   0.3383    
## MD_rh_mlf     -0.197026   0.117457  -1.677   0.0997 .  
## age:MD_lh_mlf -0.006023   0.007117  -0.846   0.4014    
## age:MD_rh_mlf  0.009028   0.007042   1.282   0.2057    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2018 on 50 degrees of freedom
## Multiple R-squared:  0.1233, Adjusted R-squared:  0.03561 
## F-statistic: 1.406 on 5 and 50 DF,  p-value: 0.2382
## 
## 
## Summary for SUB1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.141812 -0.022149  0.007612  0.030978  0.058814 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    9.496e-01  2.115e-02  44.909   <2e-16 ***
## age            6.775e-05  1.271e-03   0.053    0.958    
## MD_lh_mlf      1.728e-02  2.575e-02   0.671    0.505    
## MD_rh_mlf     -2.318e-02  2.631e-02  -0.881    0.382    
## age:MD_lh_mlf -1.089e-03  1.594e-03  -0.683    0.498    
## age:MD_rh_mlf  8.150e-04  1.577e-03   0.517    0.608    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04519 on 50 degrees of freedom
## Multiple R-squared:  0.06031,    Adjusted R-squared:  -0.03365 
## F-statistic: 0.6419 on 5 and 50 DF,  p-value: 0.6688
## 
## 
## Summary for SUB2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.46965 -0.03713  0.02813  0.07878  0.18761 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.826093   0.060616  13.628   <2e-16 ***
## age            0.001520   0.003643   0.417   0.6783    
## MD_lh_mlf      0.036089   0.073804   0.489   0.6270    
## MD_rh_mlf     -0.140031   0.075409  -1.857   0.0692 .  
## age:MD_lh_mlf -0.001168   0.004569  -0.256   0.7994    
## age:MD_rh_mlf  0.005276   0.004521   1.167   0.2487    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1296 on 50 degrees of freedom
## Multiple R-squared:  0.1554, Adjusted R-squared:  0.0709 
## F-statistic: 1.839 on 5 and 50 DF,  p-value: 0.1221
## 
## 
## Summary for SUB3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63085 -0.20301  0.04268  0.18095  0.41680 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.697815   0.126360   5.522  1.2e-06 ***
## age           -0.002111   0.007593  -0.278    0.782    
## MD_lh_mlf      0.142601   0.153852   0.927    0.358    
## MD_rh_mlf     -0.107457   0.157198  -0.684    0.497    
## age:MD_lh_mlf -0.007479   0.009525  -0.785    0.436    
## age:MD_rh_mlf  0.002888   0.009424   0.306    0.761    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2701 on 50 degrees of freedom
## Multiple R-squared:  0.04923,    Adjusted R-squared:  -0.04584 
## F-statistic: 0.5178 on 5 and 50 DF,  p-value: 0.7615
## 
## 
## Summary for MUL1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.16667 -0.02255  0.01112  0.03807  0.05517 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.9157063  0.0236828  38.665   <2e-16 ***
## age            0.0024236  0.0014232   1.703   0.0948 .  
## MD_lh_mlf      0.0043794  0.0288356   0.152   0.8799    
## MD_rh_mlf     -0.0146729  0.0294626  -0.498   0.6207    
## age:MD_lh_mlf -0.0006445  0.0017853  -0.361   0.7196    
## age:MD_rh_mlf  0.0014098  0.0017664   0.798   0.4286    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05062 on 50 degrees of freedom
## Multiple R-squared:  0.06801,    Adjusted R-squared:  -0.02519 
## F-statistic: 0.7297 on 5 and 50 DF,  p-value: 0.6045
## 
## 
## Summary for MUL2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51142 -0.08140  0.00405  0.13749  0.28081 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.635336   0.086532   7.342 1.75e-09 ***
## age            0.009604   0.005200   1.847   0.0707 .  
## MD_lh_mlf      0.101896   0.105359   0.967   0.3381    
## MD_rh_mlf     -0.218139   0.107650  -2.026   0.0481 *  
## age:MD_lh_mlf -0.005741   0.006523  -0.880   0.3830    
## age:MD_rh_mlf  0.009875   0.006454   1.530   0.1323    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1849 on 50 degrees of freedom
## Multiple R-squared:  0.1865, Adjusted R-squared:  0.1051 
## F-statistic: 2.292 on 5 and 50 DF,  p-value: 0.05948
## 
## 
## Summary for MUL3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5533 -0.1610 -0.0099  0.1759  0.5052 
## 
## Coefficients:
##                 Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    0.0977152  0.1324755   0.738  0.46420   
## age            0.0267665  0.0079610   3.362  0.00149 **
## MD_lh_mlf      0.0024295  0.1612986   0.015  0.98804   
## MD_rh_mlf      0.0835507  0.1648060   0.507  0.61441   
## age:MD_lh_mlf -0.0052625  0.0099863  -0.527  0.60054   
## age:MD_rh_mlf -0.0008522  0.0098806  -0.086  0.93161   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2831 on 50 degrees of freedom
## Multiple R-squared:  0.2299, Adjusted R-squared:  0.1529 
## F-statistic: 2.985 on 5 and 50 DF,  p-value: 0.01959
## 
## 
## Summary for DIV1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40153 -0.03249  0.02749  0.05767  0.13302 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.850406   0.048028  17.707   <2e-16 ***
## age            0.004497   0.002886   1.558   0.1255    
## MD_lh_mlf      0.077886   0.058477   1.332   0.1889    
## MD_rh_mlf     -0.114462   0.059749  -1.916   0.0611 .  
## age:MD_lh_mlf -0.004230   0.003620  -1.168   0.2482    
## age:MD_rh_mlf  0.006337   0.003582   1.769   0.0830 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1026 on 50 degrees of freedom
## Multiple R-squared:  0.1008, Adjusted R-squared:  0.01084 
## F-statistic: 1.121 on 5 and 50 DF,  p-value: 0.3616
## 
## 
## Summary for DIV2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.55920 -0.13610  0.03164  0.17648  0.34216 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    0.630264   0.106167   5.937 2.75e-07 ***
## age            0.011038   0.006380   1.730  0.08978 .  
## MD_lh_mlf      0.196486   0.129266   1.520  0.13481    
## MD_rh_mlf     -0.384580   0.132077  -2.912  0.00536 ** 
## age:MD_lh_mlf -0.014375   0.008003  -1.796  0.07851 .  
## age:MD_rh_mlf  0.022449   0.007918   2.835  0.00659 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2269 on 50 degrees of freedom
## Multiple R-squared:  0.2085, Adjusted R-squared:  0.1293 
## F-statistic: 2.634 on 5 and 50 DF,  p-value: 0.03437
## 
## 
## Summary for DIV3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63427 -0.23068  0.03154  0.24283  0.45928 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)    0.410785   0.149913   2.740  0.00849 **
## age            0.011375   0.009009   1.263  0.21256   
## MD_lh_mlf     -0.062207   0.182530  -0.341  0.73468   
## MD_rh_mlf     -0.004639   0.186499  -0.025  0.98025   
## age:MD_lh_mlf -0.001157   0.011301  -0.102  0.91886   
## age:MD_rh_mlf  0.001883   0.011181   0.168  0.86692   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3204 on 50 degrees of freedom
## Multiple R-squared:  0.08257,    Adjusted R-squared:  -0.009173 
## F-statistic:   0.9 on 5 and 50 DF,  p-value: 0.4885
## 
## 
## Summary for RT_ADD1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.80420 -0.36659  0.06126  0.27844  2.40511 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    2.75185    0.25436  10.819 1.07e-14 ***
## age           -0.06534    0.01529  -4.275 8.59e-05 ***
## MD_lh_mlf     -0.22066    0.30970  -0.712    0.479    
## MD_rh_mlf      0.28443    0.31644   0.899    0.373    
## age:MD_lh_mlf  0.01280    0.01917   0.668    0.508    
## age:MD_rh_mlf -0.01397    0.01897  -0.736    0.465    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5436 on 50 degrees of freedom
## Multiple R-squared:  0.3011, Adjusted R-squared:  0.2312 
## F-statistic: 4.308 on 5 and 50 DF,  p-value: 0.002456
## 
## 
## Summary for RT_ADD2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7006 -1.1577 -0.0887  0.6728  3.6670 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    7.230173   0.765425   9.446 1.06e-12 ***
## age           -0.151716   0.045997  -3.298   0.0018 ** 
## MD_lh_mlf     -0.254286   0.931961  -0.273   0.7861    
## MD_rh_mlf      0.256597   0.952226   0.269   0.7887    
## age:MD_lh_mlf  0.014604   0.057699   0.253   0.8012    
## age:MD_rh_mlf -0.004543   0.057089  -0.080   0.9369    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.636 on 50 degrees of freedom
## Multiple R-squared:  0.2192, Adjusted R-squared:  0.1411 
## F-statistic: 2.807 on 5 and 50 DF,  p-value: 0.02603
## 
## 
## Summary for RT_ADD3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.6109 -1.6611 -0.4984  1.1902  8.7478 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   10.80964    1.38156   7.824 3.11e-10 ***
## age           -0.16011    0.08302  -1.929   0.0595 .  
## MD_lh_mlf      1.64055    1.68215   0.975   0.3341    
## MD_rh_mlf     -2.02871    1.71873  -1.180   0.2434    
## age:MD_lh_mlf -0.05453    0.10414  -0.524   0.6028    
## age:MD_rh_mlf  0.10725    0.10304   1.041   0.3030    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.953 on 50 degrees of freedom
## Multiple R-squared:  0.1561, Adjusted R-squared:  0.07171 
## F-statistic:  1.85 on 5 and 50 DF,  p-value: 0.1202
## 
## 
## Summary for RT_SUB1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2829 -0.5360 -0.2936  0.3368  9.0256 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.418087   0.666256   5.130 4.73e-06 ***
## age           -0.082496   0.040038  -2.060   0.0446 *  
## MD_lh_mlf     -0.062056   0.811215  -0.076   0.9393    
## MD_rh_mlf      0.528874   0.828855   0.638   0.5263    
## age:MD_lh_mlf  0.009264   0.050224   0.184   0.8544    
## age:MD_rh_mlf -0.027480   0.049692  -0.553   0.5827    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.424 on 50 degrees of freedom
## Multiple R-squared:  0.1088, Adjusted R-squared:  0.01963 
## F-statistic:  1.22 on 5 and 50 DF,  p-value: 0.3135
## 
## 
## Summary for RT_SUB2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1029 -1.3788 -0.6562  1.2342  9.8200 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    8.16941    1.15183   7.093  4.3e-09 ***
## age           -0.12701    0.06922  -1.835   0.0725 .  
## MD_lh_mlf     -0.19692    1.40243  -0.140   0.8889    
## MD_rh_mlf     -0.62421    1.43293  -0.436   0.6650    
## age:MD_lh_mlf  0.02426    0.08683   0.279   0.7811    
## age:MD_rh_mlf  0.03359    0.08591   0.391   0.6975    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.462 on 50 degrees of freedom
## Multiple R-squared:  0.08981,    Adjusted R-squared:  -0.00121 
## F-statistic: 0.9867 on 5 and 50 DF,  p-value: 0.4353
## 
## 
## Summary for RT_SUB3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.8429  -3.2063  -0.9202   2.1233  13.3163 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    17.8007     2.5754   6.912 8.24e-09 ***
## age            -0.3481     0.1548  -2.249   0.0289 *  
## MD_lh_mlf       3.1832     3.1357   1.015   0.3149    
## MD_rh_mlf      -6.6287     3.2039  -2.069   0.0437 *  
## age:MD_lh_mlf  -0.1512     0.1941  -0.779   0.4398    
## age:MD_rh_mlf   0.3083     0.1921   1.605   0.1148    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.504 on 50 degrees of freedom
## Multiple R-squared:  0.1842, Adjusted R-squared:  0.1026 
## F-statistic: 2.257 on 5 and 50 DF,  p-value: 0.06289
## 
## 
## Summary for RT_MUL1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3418 -0.5935 -0.1527  0.4242  2.5174 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    3.84690    0.41969   9.166 2.77e-12 ***
## age           -0.10576    0.02522  -4.193 0.000112 ***
## MD_lh_mlf     -0.82295    0.51101  -1.610 0.113594    
## MD_rh_mlf      0.84213    0.52212   1.613 0.113058    
## age:MD_lh_mlf  0.04528    0.03164   1.431 0.158610    
## age:MD_rh_mlf -0.04318    0.03130  -1.379 0.173892    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.897 on 50 degrees of freedom
## Multiple R-squared:  0.303,  Adjusted R-squared:  0.2333 
## F-statistic: 4.346 on 5 and 50 DF,  p-value: 0.002316
## 
## 
## Summary for RT_MUL2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.9986 -2.0597 -0.9499  1.2303 11.1527 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   12.15114    1.54474   7.866 2.68e-10 ***
## age           -0.29160    0.09283  -3.141  0.00283 ** 
## MD_lh_mlf     -0.36282    1.88083  -0.193  0.84781    
## MD_rh_mlf     -0.36968    1.92173  -0.192  0.84823    
## age:MD_lh_mlf  0.03297    0.11645   0.283  0.77822    
## age:MD_rh_mlf  0.02563    0.11521   0.222  0.82485    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.302 on 50 degrees of freedom
## Multiple R-squared:  0.1978, Adjusted R-squared:  0.1176 
## F-statistic: 2.465 on 5 and 50 DF,  p-value: 0.04506
## 
## 
## Summary for RT_MUL3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.2024  -3.0038  -0.4117   2.6430  14.0486 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   21.73450    2.65736   8.179  8.8e-11 ***
## age           -0.47394    0.15969  -2.968  0.00459 ** 
## MD_lh_mlf      2.73331    3.23553   0.845  0.40226    
## MD_rh_mlf     -6.21328    3.30588  -1.879  0.06602 .  
## age:MD_lh_mlf -0.07772    0.20032  -0.388  0.69969    
## age:MD_rh_mlf  0.25746    0.19820   1.299  0.19989    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.68 on 50 degrees of freedom
## Multiple R-squared:  0.2375, Adjusted R-squared:  0.1612 
## F-statistic: 3.115 on 5 and 50 DF,  p-value: 0.01593
## 
## 
## Summary for RT_DIV1_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4827 -0.8712 -0.2528  0.5052 10.4690 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    4.21583    0.79370   5.312 2.51e-06 ***
## age           -0.11362    0.04770  -2.382   0.0211 *  
## MD_lh_mlf     -0.85141    0.96639  -0.881   0.3825    
## MD_rh_mlf      1.02106    0.98740   1.034   0.3061    
## age:MD_lh_mlf  0.05015    0.05983   0.838   0.4059    
## age:MD_rh_mlf -0.05226    0.05920  -0.883   0.3816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.696 on 50 degrees of freedom
## Multiple R-squared:   0.13,  Adjusted R-squared:  0.04301 
## F-statistic: 1.494 on 5 and 50 DF,  p-value: 0.2085
## 
## 
## Summary for RT_DIV2_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0969 -2.3017 -0.7351  1.4961 12.6145 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)   13.12911    1.97425   6.650 2.12e-08 ***
## age           -0.29518    0.11864  -2.488   0.0162 *  
## MD_lh_mlf     -0.07006    2.40380  -0.029   0.9769    
## MD_rh_mlf      0.27384    2.45607   0.111   0.9117    
## age:MD_lh_mlf  0.03863    0.14882   0.260   0.7963    
## age:MD_rh_mlf -0.01705    0.14725  -0.116   0.9083    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.22 on 50 degrees of freedom
## Multiple R-squared:  0.145,  Adjusted R-squared:  0.05946 
## F-statistic: 1.695 on 5 and 50 DF,  p-value: 0.153
## 
## 
## Summary for RT_DIV3_MD_lh_mlf_MD_rh_mlf :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.9491  -3.4524  -0.2718   3.2149  16.1580 
## 
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept)    15.5558     2.5675   6.059 1.77e-07 ***
## age            -0.2049     0.1543  -1.328  0.19011    
## MD_lh_mlf      -9.5756     3.1262  -3.063  0.00352 ** 
## MD_rh_mlf       5.6325     3.1941   1.763  0.08395 .  
## age:MD_lh_mlf   0.5009     0.1935   2.588  0.01260 *  
## age:MD_rh_mlf  -0.2934     0.1915  -1.532  0.13184    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.488 on 50 degrees of freedom
## Multiple R-squared:  0.1875, Adjusted R-squared:  0.1062 
## F-statistic: 2.307 on 5 and 50 DF,  p-value: 0.05804
for (model_name in names(standardized_results_list)) {
  cat("\nSummary for", model_name, ":\n")
  print(standardized_results_list[[model_name]])
}
## 
## Summary for ADD1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.157347 -0.015635  0.006205  0.025858  0.057578 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.8910633           NA  0.0194218  45.879   <2e-16 ***
## age            0.0029732    0.3413644  0.0011509   2.583   0.0128 *  
## FA_lh_mlf     -0.0449507   -1.0150969  0.0243582  -1.845   0.0709 .  
## FA_rh_mlf     -0.0013297   -0.0300274  0.0255541  -0.052   0.9587    
## age:FA_lh_mlf  0.0029356    1.0789316  0.0015001   1.957   0.0560 .  
## age:FA_rh_mlf -0.0003155   -0.1146717  0.0016005  -0.197   0.8445    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04176 on 50 degrees of freedom
## Multiple R-squared:  0.1914, Adjusted R-squared:  0.1105 
## F-statistic: 2.367 on 5 and 50 DF,  p-value: 0.05275
## 
## 
## Summary for ADD2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.29465 -0.06488  0.01612  0.07737  0.20461 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.786157           NA   0.053064  14.815   <2e-16 ***
## age            0.004413     0.193616   0.003144   1.403    0.167    
## FA_lh_mlf     -0.103441    -0.892713   0.066551  -1.554    0.126    
## FA_rh_mlf     -0.041496    -0.358117   0.069818  -0.594    0.555    
## age:FA_lh_mlf  0.006662     0.935730   0.004099   1.625    0.110    
## age:FA_rh_mlf  0.001666     0.231377   0.004373   0.381    0.705    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1141 on 50 degrees of freedom
## Multiple R-squared:  0.1185, Adjusted R-squared:  0.0303 
## F-statistic: 1.344 on 5 and 50 DF,  p-value: 0.2615
## 
## 
## Summary for ADD3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41864 -0.15570  0.02579  0.14116  0.33988 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.639927           NA   0.092482   6.919 8.02e-09 ***
## age            0.006703     0.165856   0.005480   1.223    0.227    
## FA_lh_mlf      0.119150     0.579845   0.115988   1.027    0.309    
## FA_rh_mlf     -0.180300    -0.877435   0.121683  -1.482    0.145    
## age:FA_lh_mlf -0.003324    -0.263299   0.007143  -0.465    0.644    
## age:FA_rh_mlf  0.007300     0.571795   0.007621   0.958    0.343    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1989 on 50 degrees of freedom
## Multiple R-squared:  0.1485, Adjusted R-squared:  0.0634 
## F-statistic: 1.745 on 5 and 50 DF,  p-value: 0.1417
## 
## 
## Summary for SUB1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.113027 -0.023330  0.005069  0.030591  0.088275 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9393790           NA  0.0205105  45.800   <2e-16 ***
## age            0.0006756    0.0772662  0.0012154   0.556    0.581    
## FA_lh_mlf      0.0075278    0.1693428  0.0257235   0.293    0.771    
## FA_rh_mlf     -0.0441038   -0.9921439  0.0269865  -1.634    0.108    
## age:FA_lh_mlf -0.0006340   -0.2321280  0.0015842  -0.400    0.691    
## age:FA_rh_mlf  0.0021546    0.7801598  0.0016902   1.275    0.208    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0441 on 50 degrees of freedom
## Multiple R-squared:  0.1051, Adjusted R-squared:  0.01564 
## F-statistic: 1.175 on 5 and 50 DF,  p-value: 0.3347
## 
## 
## Summary for SUB2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.41473 -0.04313  0.01689  0.06091  0.29791 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.804063           NA   0.061409  13.094   <2e-16 ***
## age            0.002225     0.084153   0.003639   0.611   0.5437    
## FA_lh_mlf      0.008169     0.060781   0.077017   0.106   0.9159    
## FA_rh_mlf     -0.144510    -1.075161   0.080798  -1.789   0.0798 .  
## age:FA_lh_mlf  0.001252     0.151646   0.004743   0.264   0.7928    
## age:FA_rh_mlf  0.006471     0.774981   0.005060   1.279   0.2069    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.132 on 50 degrees of freedom
## Multiple R-squared:  0.1225, Adjusted R-squared:  0.0348 
## F-statistic: 1.397 on 5 and 50 DF,  p-value: 0.2417
## 
## 
## Summary for SUB3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.62630 -0.17256  0.01021  0.18353  0.45203 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.693050           NA   0.121010   5.727 5.79e-07 ***
## age           -0.002745    -0.052845   0.007171  -0.383   0.7035    
## FA_lh_mlf     -0.054525    -0.206469   0.151766  -0.359   0.7209    
## FA_rh_mlf     -0.289448    -1.096045   0.159217  -1.818   0.0751 .  
## age:FA_lh_mlf  0.006939     0.427631   0.009347   0.742   0.4613    
## age:FA_rh_mlf  0.015547     0.947585   0.009972   1.559   0.1253    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2602 on 50 degrees of freedom
## Multiple R-squared:  0.1174, Adjusted R-squared:  0.02914 
## F-statistic:  1.33 on 5 and 50 DF,  p-value: 0.2668
## 
## 
## Summary for MUL1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.151233 -0.023314  0.008036  0.038144  0.074392 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9208457           NA  0.0230348  39.976   <2e-16 ***
## age            0.0021032    0.2138989  0.0013650   1.541    0.130    
## FA_lh_mlf      0.0141810    0.2836663  0.0288894   0.491    0.626    
## FA_rh_mlf     -0.0031023   -0.0620565  0.0303078  -0.102    0.919    
## age:FA_lh_mlf -0.0006905   -0.2247834  0.0017792  -0.388    0.700    
## age:FA_rh_mlf -0.0006834   -0.2200355  0.0018982  -0.360    0.720    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04953 on 50 degrees of freedom
## Multiple R-squared:  0.1076, Adjusted R-squared:  0.01832 
## F-statistic: 1.205 on 5 and 50 DF,  p-value: 0.3204
## 
## 
## Summary for MUL2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.48955 -0.08663  0.00852  0.14219  0.27849 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.6036941           NA  0.0897636   6.725 1.61e-08 ***
## age            0.0109027    0.2835326  0.0053192   2.050   0.0457 *  
## FA_lh_mlf      0.0092279    0.0472003  0.1125782   0.082   0.9350    
## FA_rh_mlf     -0.1346056   -0.6885021  0.1181056  -1.140   0.2598    
## age:FA_lh_mlf -0.0004945   -0.0411617  0.0069333  -0.071   0.9434    
## age:FA_rh_mlf  0.0067314    0.5542079  0.0073971   0.910   0.3672    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.193 on 50 degrees of freedom
## Multiple R-squared:  0.1139, Adjusted R-squared:  0.02526 
## F-statistic: 1.285 on 5 and 50 DF,  p-value: 0.2852
## 
## 
## Summary for MUL3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.54206 -0.14153 -0.00524  0.18143  0.50304 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)   
## (Intercept)    0.183311           NA   0.129026   1.421  0.16160   
## age            0.021964     0.362994   0.007646   2.873  0.00596 **
## FA_lh_mlf      0.106501     0.346199   0.161819   0.658  0.51346   
## FA_rh_mlf      0.021119     0.068650   0.169764   0.124  0.90150   
## age:FA_lh_mlf  0.000179     0.009472   0.009966   0.018  0.98574   
## age:FA_rh_mlf -0.006697    -0.350421   0.010632  -0.630  0.53164   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2774 on 50 degrees of freedom
## Multiple R-squared:  0.2606, Adjusted R-squared:  0.1866 
## F-statistic: 3.524 on 5 and 50 DF,  p-value: 0.008325
## 
## 
## Summary for DIV1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.31771 -0.02466  0.00914  0.05483  0.19063 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.8468724           NA  0.0457124  18.526   <2e-16 ***
## age            0.0042453    0.2091260  0.0027088   1.567   0.1234    
## FA_lh_mlf      0.0045921    0.0444929  0.0573308   0.080   0.9365    
## FA_rh_mlf     -0.1344924   -1.3030869  0.0601457  -2.236   0.0298 *  
## age:FA_lh_mlf -0.0005079   -0.0800905  0.0035308  -0.144   0.8862    
## age:FA_rh_mlf  0.0068926    1.0749306  0.0037670   1.830   0.0733 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0983 on 50 degrees of freedom
## Multiple R-squared:  0.1754, Adjusted R-squared:  0.09297 
## F-statistic: 2.127 on 5 and 50 DF,  p-value: 0.07736
## 
## 
## Summary for DIV2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.58961 -0.13072  0.02882  0.18325  0.37085 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.635655           NA   0.113210   5.615 8.63e-07 ***
## age            0.008855     0.185133   0.006709   1.320    0.193    
## FA_lh_mlf     -0.105032    -0.431908   0.141984  -0.740    0.463    
## FA_rh_mlf     -0.096527    -0.396931   0.148955  -0.648    0.520    
## age:FA_lh_mlf  0.008489     0.568102   0.008744   0.971    0.336    
## age:FA_rh_mlf  0.003269     0.216403   0.009329   0.350    0.727    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2434 on 50 degrees of freedom
## Multiple R-squared:  0.089,  Adjusted R-squared:  -0.002101 
## F-statistic: 0.9769 on 5 and 50 DF,  p-value: 0.4411
## 
## 
## Summary for DIV3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.56726 -0.25398  0.05415  0.20112  0.47227 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)  
## (Intercept)    0.397038           NA   0.150597   2.636   0.0111 *
## age            0.011882     0.189403   0.008924   1.331   0.1891  
## FA_lh_mlf     -0.101796    -0.319160   0.188873  -0.539   0.5923  
## FA_rh_mlf      0.166260     0.521272   0.198146   0.839   0.4054  
## age:FA_lh_mlf  0.008200     0.418433   0.011632   0.705   0.4841  
## age:FA_rh_mlf -0.012496    -0.630638   0.012410  -1.007   0.3188  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3238 on 50 degrees of freedom
## Multiple R-squared:  0.06289,    Adjusted R-squared:  -0.03082 
## F-statistic: 0.6711 on 5 and 50 DF,  p-value: 0.6472
## 
## 
## Summary for RT_ADD1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.8505 -0.3501  0.0438  0.2878  2.3042 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    2.7168030           NA  0.2505002  10.846 9.76e-15 ***
## age           -0.0623901   -0.5115955  0.0148440  -4.203 0.000109 ***
## FA_lh_mlf     -0.0875973   -0.1412787  0.3141680  -0.279 0.781531    
## FA_rh_mlf      0.2347075    0.3785410  0.3295930   0.712 0.479705    
## age:FA_lh_mlf -0.0008129   -0.0213364  0.0193485  -0.042 0.966657    
## age:FA_rh_mlf -0.0072102   -0.1871778  0.0206428  -0.349 0.728344    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5387 on 50 degrees of freedom
## Multiple R-squared:  0.3139, Adjusted R-squared:  0.2453 
## F-statistic: 4.575 on 5 and 50 DF,  p-value: 0.001635
## 
## 
## Summary for RT_ADD2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7671 -1.1161 -0.0237  0.5682  3.8240 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    6.86716           NA    0.72320   9.495 8.91e-13 ***
## age           -0.13234     -0.38117    0.04286  -3.088  0.00328 ** 
## FA_lh_mlf     -1.31341     -0.74404    0.90702  -1.448  0.15384    
## FA_rh_mlf      0.64958      0.36798    0.95155   0.683  0.49798    
## age:FA_lh_mlf  0.04339      0.40008    0.05586   0.777  0.44092    
## age:FA_rh_mlf -0.01990     -0.18144    0.05960  -0.334  0.73986    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.555 on 50 degrees of freedom
## Multiple R-squared:  0.2945, Adjusted R-squared:  0.2239 
## F-statistic: 4.174 on 5 and 50 DF,  p-value: 0.00302
## 
## 
## Summary for RT_ADD3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.8186 -1.4216 -0.5410  0.8326  8.1669 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   10.20496           NA    1.33041   7.671 5.39e-10 ***
## age           -0.13977     -0.23187    0.07884  -1.773   0.0823 .  
## FA_lh_mlf     -2.99782     -0.97816    1.66855  -1.797   0.0784 .  
## FA_rh_mlf     -0.35699     -0.11648    1.75047  -0.204   0.8392    
## age:FA_lh_mlf  0.12887      0.68436    0.10276   1.254   0.2156    
## age:FA_rh_mlf  0.03495      0.18356    0.10963   0.319   0.7512    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.861 on 50 degrees of freedom
## Multiple R-squared:  0.2079, Adjusted R-squared:  0.1287 
## F-statistic: 2.624 on 5 and 50 DF,  p-value: 0.03491
## 
## 
## Summary for RT_SUB1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.1364 -0.5200 -0.1037  0.2896  8.0782 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.55979           NA    0.63326   5.621 8.43e-07 ***
## age           -0.08695     -0.30737    0.03753  -2.317   0.0246 *  
## FA_lh_mlf      0.04642      0.03227    0.79421   0.058   0.9536    
## FA_rh_mlf      1.33052      0.92514    0.83320   1.597   0.1166    
## age:FA_lh_mlf -0.00964     -0.10909    0.04891  -0.197   0.8446    
## age:FA_rh_mlf -0.05831     -0.65260    0.05218  -1.117   0.2692    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.362 on 50 degrees of freedom
## Multiple R-squared:  0.185,  Adjusted R-squared:  0.1035 
## F-statistic:  2.27 on 5 and 50 DF,  p-value: 0.06157
## 
## 
## Summary for RT_SUB2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.4549 -1.6739 -0.5684  1.4405  9.4950 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    7.959324           NA   1.137687   6.996 6.09e-09 ***
## age           -0.116549    -0.240848   0.067416  -1.729    0.090 .  
## FA_lh_mlf     -0.470063    -0.191057   1.426845  -0.329    0.743    
## FA_rh_mlf      1.029863     0.418589   1.496900   0.688    0.495    
## age:FA_lh_mlf  0.001792     0.011853   0.087874   0.020    0.984    
## age:FA_rh_mlf -0.040673    -0.266096   0.093752  -0.434    0.666    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.446 on 50 degrees of freedom
## Multiple R-squared:  0.1012, Adjusted R-squared:  0.0113 
## F-statistic: 1.126 on 5 and 50 DF,  p-value: 0.359
## 
## 
## Summary for RT_SUB3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.2323  -3.2481  -0.6272   2.4753  14.2244 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    15.5611           NA     2.5074   6.206 1.05e-07 ***
## age            -0.2483      -0.2173     0.1486  -1.671   0.1009    
## FA_lh_mlf      -5.6021      -0.9642     3.1446  -1.781   0.0809 .  
## FA_rh_mlf      -1.5578      -0.2681     3.2990  -0.472   0.6388    
## age:FA_lh_mlf   0.2418       0.6773     0.1937   1.249   0.2177    
## age:FA_rh_mlf   0.1030       0.2854     0.2066   0.499   0.6202    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.392 on 50 degrees of freedom
## Multiple R-squared:  0.2172, Adjusted R-squared:  0.139 
## F-statistic: 2.775 on 5 and 50 DF,  p-value: 0.02741
## 
## 
## Summary for RT_MUL1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4574 -0.6408 -0.1239  0.4748  2.8092 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.78211           NA    0.41959   9.014 4.69e-12 ***
## age           -0.09901     -0.49137    0.02486  -3.982 0.000222 ***
## FA_lh_mlf     -0.01276     -0.01245    0.52624  -0.024 0.980758    
## FA_rh_mlf      0.68232      0.66606    0.55207   1.236 0.222263    
## age:FA_lh_mlf -0.00646     -0.10263    0.03241  -0.199 0.842815    
## age:FA_rh_mlf -0.03155     -0.49578    0.03458  -0.913 0.365864    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9023 on 50 degrees of freedom
## Multiple R-squared:  0.2948, Adjusted R-squared:  0.2243 
## F-statistic:  4.18 on 5 and 50 DF,  p-value: 0.002989
## 
## 
## Summary for RT_MUL2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -5.788 -2.052  0.054  1.206  7.581 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   11.15799           NA    1.43528   7.774 3.72e-10 ***
## age           -0.24141     -0.34923    0.08505  -2.838  0.00654 ** 
## FA_lh_mlf     -3.34712     -0.95234    1.80008  -1.859  0.06886 .  
## FA_rh_mlf      1.73070      0.49243    1.88846   0.916  0.36383    
## age:FA_lh_mlf  0.12725      0.58926    0.11086   1.148  0.25649    
## age:FA_rh_mlf -0.06994     -0.32032    0.11828  -0.591  0.55695    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.086 on 50 degrees of freedom
## Multiple R-squared:  0.299,  Adjusted R-squared:  0.2289 
## F-statistic: 4.265 on 5 and 50 DF,  p-value: 0.002624
## 
## 
## Summary for RT_MUL3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -12.720  -2.673  -0.688   2.005  14.547 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    19.2424           NA     2.5794   7.460 1.15e-09 ***
## age            -0.3597      -0.2949     0.1529  -2.353   0.0226 *  
## FA_lh_mlf      -5.8570      -0.9444     3.2350  -1.810   0.0762 .  
## FA_rh_mlf      -2.0834      -0.3359     3.3939  -0.614   0.5421    
## age:FA_lh_mlf   0.2320       0.6088     0.1992   1.164   0.2498    
## age:FA_rh_mlf   0.1769       0.4590     0.2126   0.832   0.4093    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.547 on 50 degrees of freedom
## Multiple R-squared:  0.2728, Adjusted R-squared:  0.2001 
## F-statistic: 3.751 on 5 and 50 DF,  p-value: 0.005823
## 
## 
## Summary for RT_DIV1_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.8978 -0.6983 -0.0363  0.4806  8.8696 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    4.48411           NA    0.74465   6.022 2.03e-07 ***
## age           -0.12254     -0.35928    0.04413  -2.777   0.0077 ** 
## FA_lh_mlf      0.88881      0.51256    0.93392   0.952   0.3458    
## FA_rh_mlf      1.34063      0.77310    0.97977   1.368   0.1773    
## age:FA_lh_mlf -0.05240     -0.49182    0.05752  -0.911   0.3666    
## age:FA_rh_mlf -0.05810     -0.53932    0.06136  -0.947   0.3483    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.601 on 50 degrees of freedom
## Multiple R-squared:  0.2249, Adjusted R-squared:  0.1474 
## F-statistic: 2.901 on 5 and 50 DF,  p-value: 0.02241
## 
## 
## Summary for RT_DIV2_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.5972 -2.3927 -0.4251  1.0468 12.0751 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   12.18886           NA    1.88099   6.480 3.91e-08 ***
## age           -0.24535     -0.28670    0.11146  -2.201   0.0324 *  
## FA_lh_mlf     -2.33658     -0.53703    2.35906  -0.990   0.3267    
## FA_rh_mlf     -1.23445     -0.28372    2.47489  -0.499   0.6201    
## age:FA_lh_mlf  0.05875      0.21976    0.14529   0.404   0.6877    
## age:FA_rh_mlf  0.10451      0.38662    0.15500   0.674   0.5033    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.045 on 50 degrees of freedom
## Multiple R-squared:  0.2144, Adjusted R-squared:  0.1358 
## F-statistic: 2.729 on 5 and 50 DF,  p-value: 0.02953
## 
## 
## Summary for RT_DIV3_FA_lh_mlf_FA_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.4693  -3.7415  -0.3158   2.6711  17.3905 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    15.4814           NA     2.7402   5.650 7.63e-07 ***
## age            -0.1864      -0.1633     0.1624  -1.148    0.257    
## FA_lh_mlf       4.3812       0.7548     3.4367   1.275    0.208    
## FA_rh_mlf      -1.3437      -0.2315     3.6054  -0.373    0.711    
## age:FA_lh_mlf  -0.2311      -0.6478     0.2117  -1.092    0.280    
## age:FA_rh_mlf   0.1063       0.2947     0.2258   0.471    0.640    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.892 on 50 degrees of freedom
## Multiple R-squared:  0.0632, Adjusted R-squared:  -0.03048 
## F-statistic: 0.6747 on 5 and 50 DF,  p-value: 0.6445
## 
## 
## Summary for ADD1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.176022 -0.017460  0.004908  0.026000  0.061633 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9010815           NA  0.0195696  46.045   <2e-16 ***
## age            0.0025458    0.2922908  0.0011821   2.154   0.0361 *  
## AD_lh_mlf      0.0164281    0.3709874  0.0264715   0.621   0.5377    
## AD_rh_mlf      0.0021655    0.0489022  0.0249790   0.087   0.9313    
## age:AD_lh_mlf -0.0009046   -0.3234183  0.0017882  -0.506   0.6152    
## age:AD_rh_mlf -0.0007756   -0.2751513  0.0017163  -0.452   0.6533    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.0424 on 50 degrees of freedom
## Multiple R-squared:  0.1667, Adjusted R-squared:  0.0834 
## F-statistic: 2.001 on 5 and 50 DF,  p-value: 0.09461
## 
## 
## Summary for ADD2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33652 -0.03951  0.01142  0.06503  0.20017 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.805146           NA   0.053399  15.078   <2e-16 ***
## age            0.003999     0.175477   0.003226   1.240    0.221    
## AD_lh_mlf      0.026482     0.228544   0.072232   0.367    0.715    
## AD_rh_mlf     -0.083772    -0.722969   0.068159  -1.229    0.225    
## age:AD_lh_mlf -0.001763    -0.240870   0.004879  -0.361    0.719    
## age:AD_rh_mlf  0.004005     0.543017   0.004683   0.855    0.396    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1157 on 50 degrees of freedom
## Multiple R-squared:  0.0939, Adjusted R-squared:  0.003287 
## F-statistic: 1.036 on 5 and 50 DF,  p-value: 0.4068
## 
## 
## Summary for ADD3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38728 -0.16528  0.00608  0.15612  0.34369 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.623018           NA   0.090504   6.884 9.12e-09 ***
## age            0.008116     0.200821   0.005467   1.485   0.1439    
## AD_lh_mlf      0.138292     0.673000   0.122423   1.130   0.2640    
## AD_rh_mlf     -0.209122    -1.017695   0.115521  -1.810   0.0763 .  
## age:AD_lh_mlf -0.006197    -0.477475   0.008270  -0.749   0.4571    
## age:AD_rh_mlf  0.008896     0.680089   0.007938   1.121   0.2677    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1961 on 50 degrees of freedom
## Multiple R-squared:  0.1723, Adjusted R-squared:  0.08958 
## F-statistic: 2.082 on 5 and 50 DF,  p-value: 0.08313
## 
## 
## Summary for SUB1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.118058 -0.022622  0.007776  0.032995  0.071786 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9477602           NA  0.0199308  47.553   <2e-16 ***
## age            0.0002269    0.0259538  0.0012039   0.188    0.851    
## AD_lh_mlf      0.0218917    0.4924681  0.0269600   0.812    0.421    
## AD_rh_mlf     -0.0314175   -0.7067584  0.0254400  -1.235    0.223    
## age:AD_lh_mlf -0.0016141   -0.5748858  0.0018212  -0.886    0.380    
## age:AD_rh_mlf  0.0011914    0.4210223  0.0017480   0.682    0.499    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04318 on 50 degrees of freedom
## Multiple R-squared:  0.1423, Adjusted R-squared:  0.05656 
## F-statistic: 1.659 on 5 and 50 DF,  p-value: 0.1618
## 
## 
## Summary for SUB2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.38742 -0.05175  0.00935  0.07371  0.25717 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.828705           NA   0.057071  14.520   <2e-16 ***
## age            0.001120     0.042348   0.003447   0.325    0.747    
## AD_lh_mlf     -0.020055    -0.149207   0.077200  -0.260    0.796    
## AD_rh_mlf     -0.115915    -0.862414   0.072847  -1.591    0.118    
## age:AD_lh_mlf  0.003292     0.387738   0.005215   0.631    0.531    
## age:AD_rh_mlf  0.002882     0.336806   0.005005   0.576    0.567    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1236 on 50 degrees of freedom
## Multiple R-squared:  0.2308, Adjusted R-squared:  0.1538 
## F-statistic:     3 on 5 and 50 DF,  p-value: 0.01914
## 
## 
## Summary for SUB3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.60229 -0.18355  0.01737  0.20608  0.40372 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.708606           NA   0.123674   5.730 5.74e-07 ***
## age           -0.002518    -0.048486   0.007471  -0.337    0.737    
## AD_lh_mlf      0.080033     0.303059   0.167292   0.478    0.634    
## AD_rh_mlf     -0.126649    -0.479577   0.157860  -0.802    0.426    
## age:AD_lh_mlf -0.001496    -0.089699   0.011301  -0.132    0.895    
## age:AD_rh_mlf  0.002923     0.173900   0.010847   0.270    0.789    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2679 on 50 degrees of freedom
## Multiple R-squared:  0.06427,    Adjusted R-squared:  -0.02931 
## F-statistic: 0.6868 on 5 and 50 DF,  p-value: 0.6356
## 
## 
## Summary for MUL1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.156168 -0.032025  0.009829  0.033100  0.064797 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.918783           NA   0.023425  39.222   <2e-16 ***
## age            0.002232     0.227036   0.001415   1.578    0.121    
## AD_lh_mlf      0.016737     0.334789   0.031687   0.528    0.600    
## AD_rh_mlf     -0.026863    -0.537353   0.029900  -0.898    0.373    
## age:AD_lh_mlf -0.001427    -0.452026   0.002140  -0.667    0.508    
## age:AD_rh_mlf  0.001776     0.558033   0.002054   0.864    0.391    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05075 on 50 degrees of freedom
## Multiple R-squared:  0.06322,    Adjusted R-squared:  -0.03046 
## F-statistic: 0.6748 on 5 and 50 DF,  p-value: 0.6445
## 
## 
## Summary for MUL2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52272 -0.08951 -0.00284  0.14295  0.27915 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.626640           NA   0.084543   7.412 1.36e-09 ***
## age            0.010051     0.261375   0.005107   1.968   0.0546 .  
## AD_lh_mlf      0.075915     0.388301   0.114359   0.664   0.5099    
## AD_rh_mlf     -0.198234    -1.013957   0.107912  -1.837   0.0722 .  
## age:AD_lh_mlf -0.004670    -0.378158   0.007725  -0.604   0.5483    
## age:AD_rh_mlf  0.009063     0.728218   0.007415   1.222   0.2273    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1832 on 50 degrees of freedom
## Multiple R-squared:  0.2022, Adjusted R-squared:  0.1224 
## F-statistic: 2.534 on 5 and 50 DF,  p-value: 0.04036
## 
## 
## Summary for MUL3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52973 -0.16342 -0.00354  0.16533  0.55713 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)   
## (Intercept)    0.112258           NA   0.133441   0.841  0.40421   
## age            0.026142     0.432058   0.008061   3.243  0.00211 **
## AD_lh_mlf      0.113384     0.368574   0.180503   0.628  0.53276   
## AD_rh_mlf      0.031601     0.102723   0.170326   0.186  0.85356   
## age:AD_lh_mlf -0.008035    -0.413545   0.012193  -0.659  0.51291   
## age:AD_rh_mlf -0.001295    -0.066119   0.011703  -0.111  0.91235   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2891 on 50 degrees of freedom
## Multiple R-squared:  0.1972, Adjusted R-squared:  0.1169 
## F-statistic: 2.457 on 5 and 50 DF,  p-value: 0.04569
## 
## 
## Summary for DIV1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.35387 -0.03171  0.01995  0.05953  0.12224 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.854499           NA   0.045258  18.881  < 2e-16 ***
## age            0.004357     0.214634   0.002734   1.594  0.11729    
## AD_lh_mlf      0.086779     0.840792   0.061219   1.418  0.16254    
## AD_rh_mlf     -0.158974    -1.540285   0.057768  -2.752  0.00823 ** 
## age:AD_lh_mlf -0.005532    -0.848528   0.004135  -1.338  0.18708    
## age:AD_rh_mlf  0.009174     1.396271   0.003969   2.311  0.02498 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.09805 on 50 degrees of freedom
## Multiple R-squared:  0.1796, Adjusted R-squared:  0.09759 
## F-statistic:  2.19 on 5 and 50 DF,  p-value: 0.07007
## 
## 
## Summary for DIV2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.55256 -0.12697  0.01742  0.16688  0.39112 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.615628           NA   0.104353   5.899 3.13e-07 ***
## age            0.011956     0.249957   0.006304   1.897   0.0637 .  
## AD_lh_mlf      0.132594     0.545244   0.141156   0.939   0.3521    
## AD_rh_mlf     -0.386541    -1.589511   0.133197  -2.902   0.0055 ** 
## age:AD_lh_mlf -0.011459    -0.746061   0.009535  -1.202   0.2351    
## age:AD_rh_mlf  0.024264     1.567369   0.009152   2.651   0.0107 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2261 on 50 degrees of freedom
## Multiple R-squared:  0.2144, Adjusted R-squared:  0.1358 
## F-statistic: 2.729 on 5 and 50 DF,  p-value: 0.02954
## 
## 
## Summary for DIV3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.6305 -0.2777  0.0613  0.2467  0.5017 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)  
## (Intercept)    0.395490           NA   0.148619   2.661   0.0104 *
## age            0.012168     0.193970   0.008977   1.355   0.1814  
## AD_lh_mlf     -0.085473    -0.267983   0.201034  -0.425   0.6725  
## AD_rh_mlf      0.025037     0.078498   0.189699   0.132   0.8955  
## age:AD_lh_mlf  0.001641     0.081481   0.013580   0.121   0.9043  
## age:AD_rh_mlf -0.001507    -0.074228   0.013034  -0.116   0.9084  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.322 on 50 degrees of freedom
## Multiple R-squared:  0.07365,    Adjusted R-squared:  -0.01899 
## F-statistic: 0.795 on 5 and 50 DF,  p-value: 0.5584
## 
## 
## Summary for RT_ADD1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.82463 -0.33411  0.02597  0.25325  2.32156 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    2.716634           NA   0.247903  10.958 6.76e-15 ***
## age           -0.063115    -0.517538   0.014975  -4.215 0.000105 ***
## AD_lh_mlf     -0.211254    -0.340715   0.335334  -0.630 0.531575    
## AD_rh_mlf      0.272154     0.438936   0.316427   0.860 0.393847    
## age:AD_lh_mlf  0.008959     0.228770   0.022652   0.396 0.694147    
## age:AD_rh_mlf -0.009754    -0.247131   0.021742  -0.449 0.655629    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5371 on 50 degrees of freedom
## Multiple R-squared:  0.318,  Adjusted R-squared:  0.2498 
## F-statistic: 4.662 on 5 and 50 DF,  p-value: 0.001433
## 
## 
## Summary for RT_ADD2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.9945 -1.1485 -0.1579  0.5768  3.5128 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    7.1860122           NA  0.7394387   9.718 4.17e-13 ***
## age           -0.1493360   -0.4301132  0.0446664  -3.343  0.00157 ** 
## AD_lh_mlf     -0.8446375   -0.4784801  1.0002264  -0.844  0.40244    
## AD_rh_mlf      0.3479995    0.1971388  0.9438313   0.369  0.71390    
## age:AD_lh_mlf  0.0295052    0.2646296  0.0675658   0.437  0.66422    
## age:AD_rh_mlf  0.0009735    0.0086626  0.0648519   0.015  0.98808    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.602 on 50 degrees of freedom
## Multiple R-squared:  0.2514, Adjusted R-squared:  0.1765 
## F-statistic: 3.358 on 5 and 50 DF,  p-value: 0.01082
## 
## 
## Summary for RT_ADD3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -4.9808 -1.8458 -0.4902  0.9297  9.6705 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   11.12352           NA    1.38705   8.020 1.55e-10 ***
## age           -0.18176     -0.30153    0.08379  -2.169   0.0348 *  
## AD_lh_mlf     -0.40023     -0.13059    1.87624  -0.213   0.8320    
## AD_rh_mlf     -1.42897     -0.46626    1.77045  -0.807   0.4234    
## age:AD_lh_mlf  0.03460      0.17875    0.12674   0.273   0.7860    
## age:AD_rh_mlf  0.08577      0.43964    0.12165   0.705   0.4840    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.005 on 50 degrees of freedom
## Multiple R-squared:  0.1261, Adjusted R-squared:  0.0387 
## F-statistic: 1.443 on 5 and 50 DF,  p-value: 0.2254
## 
## 
## Summary for RT_SUB1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.7520 -0.6427 -0.2162  0.3337  8.3339 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.3906403           NA  0.6372341   5.321 2.43e-06 ***
## age           -0.0807715   -0.2855407  0.0384927  -2.098   0.0409 *  
## AD_lh_mlf      0.0106113    0.0073783  0.8619758   0.012   0.9902    
## AD_rh_mlf      0.9133311    0.6350581  0.8133756   1.123   0.2668    
## age:AD_lh_mlf  0.0008573    0.0094371  0.0582269   0.015   0.9883    
## age:AD_rh_mlf -0.0391234   -0.4273295  0.0558881  -0.700   0.4872    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.38 on 50 degrees of freedom
## Multiple R-squared:  0.1624, Adjusted R-squared:  0.07862 
## F-statistic: 1.939 on 5 and 50 DF,  p-value: 0.1044
## 
## 
## Summary for RT_SUB2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.2713 -1.5321 -0.6067  1.0334  9.9493 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    8.141215           NA   1.137128   7.159 3.38e-09 ***
## age           -0.128798    -0.266159   0.068689  -1.875   0.0666 .  
## AD_lh_mlf     -0.897442    -0.364766   1.538174  -0.583   0.5622    
## AD_rh_mlf      0.028579     0.011616   1.451448   0.020   0.9844    
## age:AD_lh_mlf  0.051904     0.334005   0.103904   0.500   0.6196    
## age:AD_rh_mlf  0.008145     0.052005   0.099731   0.082   0.9352    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.463 on 50 degrees of freedom
## Multiple R-squared:  0.08859,    Adjusted R-squared:  -0.002547 
## F-statistic: 0.9721 on 5 and 50 DF,  p-value: 0.444
## 
## 
## Summary for RT_SUB3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.1398  -3.2497  -0.9973   2.4507  12.0327 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   17.70524           NA    2.50021   7.081 4.47e-09 ***
## age           -0.34962     -0.30592    0.15103  -2.315   0.0248 *  
## AD_lh_mlf     -1.47559     -0.25396    3.38199  -0.436   0.6645    
## AD_rh_mlf     -4.50735     -0.77574    3.19131  -1.412   0.1640    
## age:AD_lh_mlf  0.05737      0.15634    0.22846   0.251   0.8027    
## age:AD_rh_mlf  0.21813      0.58974    0.21928   0.995   0.3246    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.416 on 50 degrees of freedom
## Multiple R-squared:   0.21,  Adjusted R-squared:  0.131 
## F-statistic: 2.658 on 5 and 50 DF,  p-value: 0.03306
## 
## 
## Summary for RT_MUL1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3029 -0.5607 -0.1714  0.4499  2.3794 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.77287           NA    0.40815   9.244 2.12e-12 ***
## age           -0.10198     -0.50611    0.02465  -4.136 0.000135 ***
## AD_lh_mlf     -0.78584     -0.76712    0.55209  -1.423 0.160834    
## AD_rh_mlf      0.89484      0.87352    0.52097   1.718 0.092046 .  
## age:AD_lh_mlf  0.04194      0.64823    0.03729   1.125 0.266108    
## age:AD_rh_mlf -0.04470     -0.68546    0.03580  -1.249 0.217569    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.8842 on 50 degrees of freedom
## Multiple R-squared:  0.3227, Adjusted R-squared:  0.255 
## F-statistic: 4.765 on 5 and 50 DF,  p-value: 0.001227
## 
## 
## Summary for RT_MUL2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.7400 -2.1399 -0.6008  0.9545  9.9783 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   12.08021           NA    1.49186   8.097 1.18e-10 ***
## age           -0.29072     -0.42055    0.09012  -3.226  0.00222 ** 
## AD_lh_mlf     -2.18103     -0.62056    2.01801  -1.081  0.28498    
## AD_rh_mlf      0.34790      0.09899    1.90423   0.183  0.85577    
## age:AD_lh_mlf  0.09813      0.44202    0.13632   0.720  0.47499    
## age:AD_rh_mlf  0.00574      0.02565    0.13084   0.044  0.96519    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.232 on 50 degrees of freedom
## Multiple R-squared:  0.2313, Adjusted R-squared:  0.1544 
## F-statistic: 3.008 on 5 and 50 DF,  p-value: 0.01887
## 
## 
## Summary for RT_MUL3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -13.0314  -3.1461  -0.6497   2.2128  12.9596 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    21.6842           NA     2.6231   8.267 6.45e-11 ***
## age            -0.4799      -0.3934     0.1584  -3.028  0.00388 ** 
## AD_lh_mlf      -2.3536      -0.3795     3.5482  -0.663  0.51017    
## AD_rh_mlf      -4.0357      -0.6508     3.3482  -1.205  0.23374    
## age:AD_lh_mlf   0.1530       0.3906     0.2397   0.638  0.52614    
## age:AD_rh_mlf   0.1766       0.4473     0.2301   0.768  0.44634    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.683 on 50 degrees of freedom
## Multiple R-squared:  0.2367, Adjusted R-squared:  0.1603 
## F-statistic: 3.101 on 5 and 50 DF,  p-value: 0.01629
## 
## 
## Summary for RT_DIV1_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.0569 -0.8110 -0.1282  0.7121  9.6008 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    4.09743           NA    0.76103   5.384 1.95e-06 ***
## age           -0.10699     -0.31368    0.04597  -2.327    0.024 *  
## AD_lh_mlf     -0.34662     -0.19989    1.02943  -0.337    0.738    
## AD_rh_mlf      1.23130      0.71006    0.97139   1.268    0.211    
## age:AD_lh_mlf  0.02248      0.20524    0.06954   0.323    0.748    
## age:AD_rh_mlf -0.05457     -0.49436    0.06675  -0.818    0.417    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.649 on 50 degrees of freedom
## Multiple R-squared:  0.1783, Adjusted R-squared:  0.09608 
## F-statistic: 2.169 on 5 and 50 DF,  p-value: 0.07238
## 
## 
## Summary for RT_DIV2_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.3227 -2.5867 -0.6478  0.8392 14.2697 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   13.28944           NA    1.95346   6.803 1.22e-08 ***
## age           -0.30529     -0.35674    0.11800  -2.587   0.0126 *  
## AD_lh_mlf     -1.48042     -0.34025    2.64241  -0.560   0.5778    
## AD_rh_mlf     -0.07573     -0.01741    2.49343  -0.030   0.9759    
## age:AD_lh_mlf  0.08217      0.29899    0.17850   0.460   0.6473    
## age:AD_rh_mlf  0.01317      0.04756    0.17133   0.077   0.9390    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.232 on 50 degrees of freedom
## Multiple R-squared:   0.14,  Adjusted R-squared:  0.05395 
## F-statistic: 1.627 on 5 and 50 DF,  p-value: 0.17
## 
## 
## Summary for RT_DIV3_AD_lh_mlf_AD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -15.4536  -2.7051  -0.7691   2.4556  17.0550 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    14.3835           NA     2.6378   5.453 1.53e-06 ***
## age            -0.1414      -0.1239     0.1593  -0.887   0.3791    
## AD_lh_mlf      -7.5310      -1.2974     3.5681  -2.111   0.0398 *  
## AD_rh_mlf       3.5314       0.6084     3.3669   1.049   0.2993    
## age:AD_lh_mlf   0.4219       1.1509     0.2410   1.751   0.0862 .  
## age:AD_rh_mlf  -0.1691      -0.4576     0.2313  -0.731   0.4683    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.714 on 50 degrees of freedom
## Multiple R-squared:  0.1189, Adjusted R-squared:  0.0308 
## F-statistic:  1.35 on 5 and 50 DF,  p-value: 0.2592
## 
## 
## Summary for ADD1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.182452 -0.020227  0.006315  0.023575  0.058412 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.8917740           NA  0.0196002  45.498   <2e-16 ***
## age            0.0029931    0.3436462  0.0011743   2.549   0.0139 *  
## RD_lh_mlf      0.0424597    0.9588452  0.0237693   1.786   0.0801 .  
## RD_rh_mlf     -0.0063609   -0.1436445  0.0269524  -0.236   0.8144    
## age:RD_lh_mlf -0.0027314   -1.0146191  0.0014127  -1.933   0.0588 .  
## age:RD_rh_mlf  0.0003832    0.1512454  0.0015321   0.250   0.8035    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04163 on 50 degrees of freedom
## Multiple R-squared:  0.1964, Adjusted R-squared:  0.116 
## F-statistic: 2.444 on 5 and 50 DF,  p-value: 0.04662
## 
## 
## Summary for ADD2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.36573 -0.05423  0.01482  0.06796  0.15964 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.794863           NA   0.054671  14.539   <2e-16 ***
## age            0.004427     0.194229   0.003275   1.351    0.183    
## RD_lh_mlf      0.100921     0.870964   0.066300   1.522    0.134    
## RD_rh_mlf     -0.093326    -0.805421   0.075179  -1.241    0.220    
## age:RD_lh_mlf -0.006056    -0.859733   0.003940  -1.537    0.131    
## age:RD_rh_mlf  0.004767     0.719084   0.004274   1.115    0.270    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1161 on 50 degrees of freedom
## Multiple R-squared:  0.08688,    Adjusted R-squared:  -0.004435 
## F-statistic: 0.9514 on 5 and 50 DF,  p-value: 0.4564
## 
## 
## Summary for ADD3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.48113 -0.17365  0.04247  0.17703  0.32968 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.618560           NA   0.097804   6.324 6.84e-08 ***
## age            0.008185     0.202527   0.005860   1.397    0.169    
## RD_lh_mlf      0.018653     0.090777   0.118608   0.157    0.876    
## RD_rh_mlf     -0.080710    -0.392778   0.134491  -0.600    0.551    
## age:RD_lh_mlf -0.002127    -0.170234   0.007049  -0.302    0.764    
## age:RD_rh_mlf  0.004062     0.345552   0.007645   0.531    0.598    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2077 on 50 degrees of freedom
## Multiple R-squared:  0.07076,    Adjusted R-squared:  -0.02216 
## F-statistic: 0.7615 on 5 and 50 DF,  p-value: 0.5818
## 
## 
## Summary for SUB1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.14931 -0.02070  0.01064  0.03121  0.05239 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9455473           NA  0.0218632  43.248   <2e-16 ***
## age            0.0002687    0.0307319  0.0013099   0.205    0.838    
## RD_lh_mlf      0.0046829    0.1053456  0.0265137   0.177    0.861    
## RD_rh_mlf      0.0017354    0.0390394  0.0300643   0.058    0.954    
## age:RD_lh_mlf -0.0003516   -0.1301231  0.0015758  -0.223    0.824    
## age:RD_rh_mlf -0.0002003   -0.0787562  0.0017090  -0.117    0.907    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04644 on 50 degrees of freedom
## Multiple R-squared:  0.007796,   Adjusted R-squared:  -0.09142 
## F-statistic: 0.07857 on 5 and 50 DF,  p-value: 0.9952
## 
## 
## Summary for SUB2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52093 -0.02886  0.03287  0.09272  0.16337 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.8157231           NA  0.0647685  12.594   <2e-16 ***
## age            0.0019845    0.0750678  0.0038804   0.511    0.611    
## RD_lh_mlf      0.0078255    0.0582223  0.0785454   0.100    0.921    
## RD_rh_mlf     -0.0657399   -0.4891082  0.0890638  -0.738    0.464    
## age:RD_lh_mlf -0.0005345   -0.0654163  0.0046682  -0.115    0.909    
## age:RD_rh_mlf  0.0025608    0.3330174  0.0050628   0.506    0.615    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1376 on 50 degrees of freedom
## Multiple R-squared:  0.04752,    Adjusted R-squared:  -0.04772 
## F-statistic: 0.4989 on 5 and 50 DF,  p-value: 0.7755
## 
## 
## Summary for SUB3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.65838 -0.16586  0.04222  0.19584  0.37584 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.693446           NA   0.127772   5.427 1.67e-06 ***
## age           -0.002406    -0.046322   0.007655  -0.314    0.755    
## RD_lh_mlf      0.083200     0.315050   0.154951   0.537    0.594    
## RD_rh_mlf      0.033013     0.125010   0.175701   0.188    0.852    
## age:RD_lh_mlf -0.005898    -0.367374   0.009209  -0.640    0.525    
## age:RD_rh_mlf -0.003402    -0.225168   0.009988  -0.341    0.735    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2714 on 50 degrees of freedom
## Multiple R-squared:  0.0398, Adjusted R-squared:  -0.05622 
## F-statistic: 0.4145 on 5 and 50 DF,  p-value: 0.8365
## 
## 
## Summary for MUL1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.162168 -0.023295  0.006575  0.040165  0.062643 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9147456           NA  0.0235266  38.881   <2e-16 ***
## age            0.0024648    0.2506687  0.0014095   1.749   0.0865 .  
## RD_lh_mlf     -0.0083766   -0.1675600  0.0285309  -0.294   0.7703    
## RD_rh_mlf      0.0031898    0.0638073  0.0323516   0.099   0.9219    
## age:RD_lh_mlf  0.0001093    0.0359568  0.0016957   0.064   0.9489    
## age:RD_rh_mlf  0.0006308    0.2205507  0.0018390   0.343   0.7330    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04997 on 50 degrees of freedom
## Multiple R-squared:  0.09157,    Adjusted R-squared:  0.0007253 
## F-statistic: 1.008 on 5 and 50 DF,  p-value: 0.4229
## 
## 
## Summary for MUL2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.52561 -0.10166  0.02307  0.12703  0.33579 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.625090           NA   0.090793   6.885 9.09e-09 ***
## age            0.010074     0.261968   0.005440   1.852   0.0699 .  
## RD_lh_mlf      0.065283     0.333922   0.110105   0.593   0.5559    
## RD_rh_mlf     -0.151922    -0.777074   0.124850  -1.217   0.2294    
## age:RD_lh_mlf -0.003843    -0.323382   0.006544  -0.587   0.5596    
## age:RD_rh_mlf  0.007219     0.645420   0.007097   1.017   0.3140    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1929 on 50 degrees of freedom
## Multiple R-squared:  0.1154, Adjusted R-squared:  0.02691 
## F-statistic: 1.304 on 5 and 50 DF,  p-value: 0.2773
## 
## 
## Summary for MUL3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.61108 -0.15658 -0.02475  0.17862  0.47835 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)   
## (Intercept)    0.121492           NA   0.130309   0.932  0.35565   
## age            0.025190     0.416317   0.007807   3.227  0.00221 **
## RD_lh_mlf     -0.087056    -0.282988   0.158027  -0.551  0.58416   
## RD_rh_mlf      0.155069     0.504076   0.179190   0.865  0.39096   
## age:RD_lh_mlf -0.001602    -0.085664   0.009392  -0.171  0.86525   
## age:RD_rh_mlf -0.003657    -0.207763   0.010186  -0.359  0.72112   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2768 on 50 degrees of freedom
## Multiple R-squared:  0.264,  Adjusted R-squared:  0.1904 
## F-statistic: 3.587 on 5 and 50 DF,  p-value: 0.007532
## 
## 
## Summary for DIV1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40804 -0.01672  0.02967  0.05637  0.10683 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.844845           NA   0.049699  16.999   <2e-16 ***
## age            0.004611     0.227126   0.002978   1.548    0.128    
## RD_lh_mlf      0.035421     0.343192   0.060270   0.588    0.559    
## RD_rh_mlf     -0.032255    -0.312513   0.068342  -0.472    0.639    
## age:RD_lh_mlf -0.001806    -0.287893   0.003582  -0.504    0.616    
## age:RD_rh_mlf  0.002240     0.379384   0.003885   0.577    0.567    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1056 on 50 degrees of freedom
## Multiple R-squared:  0.04891,    Adjusted R-squared:  -0.0462 
## F-statistic: 0.5143 on 5 and 50 DF,  p-value: 0.7642
## 
## 
## Summary for DIV2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.53569 -0.12525  0.06988  0.18164  0.35545 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.633217           NA   0.111719   5.668 7.15e-07 ***
## age            0.010400     0.217428   0.006693   1.554   0.1266    
## RD_lh_mlf      0.162568     0.668502   0.135483   1.200   0.2358    
## RD_rh_mlf     -0.297554    -1.223584   0.153626  -1.937   0.0584 .  
## age:RD_lh_mlf -0.012082    -0.817250   0.008052  -1.500   0.1398    
## age:RD_rh_mlf  0.017655     1.268997   0.008733   2.022   0.0486 *  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2373 on 50 degrees of freedom
## Multiple R-squared:  0.1343, Adjusted R-squared:  0.04773 
## F-statistic: 1.551 on 5 and 50 DF,  p-value: 0.1911
## 
## 
## Summary for DIV3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.60538 -0.22555  0.03192  0.22854  0.51545 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)   
## (Intercept)    0.414386           NA   0.151244   2.740   0.0085 **
## age            0.011168     0.178020   0.009061   1.232   0.2235   
## RD_lh_mlf     -0.049505    -0.155213   0.183415  -0.270   0.7883   
## RD_rh_mlf     -0.008763    -0.027475   0.207977  -0.042   0.9666   
## age:RD_lh_mlf -0.001861    -0.095994   0.010901  -0.171   0.8651   
## age:RD_rh_mlf  0.002901     0.158974   0.011822   0.245   0.8072   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3213 on 50 degrees of freedom
## Multiple R-squared:  0.07768,    Adjusted R-squared:  -0.01456 
## F-statistic: 0.8422 on 5 and 50 DF,  p-value: 0.5263
## 
## 
## Summary for RT_ADD1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.76793 -0.35428  0.05524  0.28011  2.44032 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    2.762262           NA   0.257889  10.711 1.52e-14 ***
## age           -0.065538    -0.537404   0.015451  -4.242 9.57e-05 ***
## RD_lh_mlf     -0.086170    -0.138976   0.312745  -0.276    0.784    
## RD_rh_mlf      0.097825     0.157774   0.354626   0.276    0.784    
## age:RD_lh_mlf  0.007542     0.200095   0.018587   0.406    0.687    
## age:RD_rh_mlf -0.006729    -0.189692   0.020159  -0.334    0.740    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5478 on 50 degrees of freedom
## Multiple R-squared:  0.2904, Adjusted R-squared:  0.2194 
## F-statistic: 4.092 on 5 and 50 DF,  p-value: 0.003423
## 
## 
## Summary for RT_ADD2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.4784 -1.2143 -0.0481  0.6604  3.6517 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    7.129055           NA   0.765772   9.310 1.69e-12 ***
## age           -0.145228    -0.418281   0.045879  -3.165  0.00264 ** 
## RD_lh_mlf      0.402150     0.227815   0.928659   0.433  0.66685    
## RD_rh_mlf     -0.245707    -0.139191   1.053021  -0.233  0.81645    
## age:RD_lh_mlf -0.009721    -0.090586   0.055193  -0.176  0.86090    
## age:RD_rh_mlf  0.014977     0.148297   0.059858   0.250  0.80345    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.627 on 50 degrees of freedom
## Multiple R-squared:  0.2281, Adjusted R-squared:  0.1509 
## F-statistic: 2.955 on 5 and 50 DF,  p-value: 0.02055
## 
## 
## Summary for RT_ADD3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -6.7087 -1.5550 -0.5678  1.2359  8.3838 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   10.42417           NA    1.36379   7.644 5.94e-10 ***
## age           -0.13915     -0.23083    0.08171  -1.703   0.0948 .  
## RD_lh_mlf      2.47354      0.80709    1.65389   1.496   0.1410    
## RD_rh_mlf     -2.14805     -0.70089    1.87537  -1.145   0.2575    
## age:RD_lh_mlf -0.08884     -0.47681    0.09830  -0.904   0.3705    
## age:RD_rh_mlf  0.10919      0.62275    0.10660   1.024   0.3106    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.897 on 50 degrees of freedom
## Multiple R-squared:  0.1878, Adjusted R-squared:  0.1065 
## F-statistic: 2.312 on 5 and 50 DF,  p-value: 0.05763
## 
## 
## Summary for RT_SUB1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2414 -0.4934 -0.2421  0.1962  9.0973 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.485993           NA   0.672721   5.182 3.95e-06 ***
## age           -0.084528    -0.298820   0.040304  -2.097    0.041 *  
## RD_lh_mlf      0.301378     0.209554   0.815815   0.369    0.713    
## RD_rh_mlf     -0.387092    -0.269153   0.925065  -0.418    0.677    
## age:RD_lh_mlf -0.007279    -0.083253   0.048486  -0.150    0.881    
## age:RD_rh_mlf  0.012318     0.149708   0.052585   0.234    0.816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.429 on 50 degrees of freedom
## Multiple R-squared:  0.1025, Adjusted R-squared:  0.01279 
## F-statistic: 1.143 on 5 and 50 DF,  p-value: 0.3505
## 
## 
## Summary for RT_SUB2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.3839 -1.4275 -0.6823  1.2556  9.5187 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    8.094376           NA   1.150247   7.037 5.25e-09 ***
## age           -0.120442    -0.248891   0.068913  -1.748   0.0867 .  
## RD_lh_mlf      0.460273     0.187078   1.394915   0.330   0.7428    
## RD_rh_mlf     -1.478704    -0.601020   1.581716  -0.935   0.3543    
## age:RD_lh_mlf -0.004394    -0.029376   0.082904  -0.053   0.9579    
## age:RD_rh_mlf  0.072442     0.514649   0.089912   0.806   0.4242    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.443 on 50 degrees of freedom
## Multiple R-squared:  0.1035, Adjusted R-squared:  0.0138 
## F-statistic: 1.154 on 5 and 50 DF,  p-value: 0.3449
## 
## 
## Summary for RT_SUB3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -11.5832  -2.8900  -0.5105   1.6923  13.0722 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    16.9189           NA     2.6257   6.443 4.46e-08 ***
## age            -0.2992      -0.2618     0.1573  -1.902   0.0629 .  
## RD_lh_mlf       4.8832       0.8404     3.1843   1.534   0.1314    
## RD_rh_mlf      -6.5970      -1.1354     3.6107  -1.827   0.0737 .  
## age:RD_lh_mlf  -0.2177      -0.6164     0.1893  -1.151   0.2554    
## age:RD_rh_mlf   0.3164       0.9517     0.2052   1.541   0.1295    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.577 on 50 degrees of freedom
## Multiple R-squared:  0.1623, Adjusted R-squared:  0.07857 
## F-statistic: 1.938 on 5 and 50 DF,  p-value: 0.1045
## 
## 
## Summary for RT_MUL1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2819 -0.6127 -0.1099  0.3941  2.5927 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.87616           NA    0.43205   8.972 5.43e-12 ***
## age           -0.10606     -0.52640    0.02588  -4.098 0.000153 ***
## RD_lh_mlf     -0.53329     -0.52058    0.52395  -1.018 0.313662    
## RD_rh_mlf      0.40694      0.39724    0.59412   0.685 0.496538    
## age:RD_lh_mlf  0.03171      0.50922    0.03114   1.018 0.313400    
## age:RD_rh_mlf -0.02320     -0.39587    0.03377  -0.687 0.495259    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.9177 on 50 degrees of freedom
## Multiple R-squared:  0.2704, Adjusted R-squared:  0.1974 
## F-statistic: 3.706 on 5 and 50 DF,  p-value: 0.006251
## 
## 
## Summary for RT_MUL2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.0745 -2.0771 -0.5475  1.2365 10.6368 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   11.83526           NA    1.53225   7.724 4.45e-10 ***
## age           -0.27122     -0.39234    0.09180  -2.954  0.00477 ** 
## RD_lh_mlf      1.18124      0.33609    1.85818   0.636  0.52787    
## RD_rh_mlf     -1.53194     -0.43588    2.10702  -0.727  0.47057    
## age:RD_lh_mlf -0.02852     -0.13350    0.11044  -0.258  0.79725    
## age:RD_rh_mlf  0.07659      0.38090    0.11977   0.639  0.52544    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.255 on 50 degrees of freedom
## Multiple R-squared:  0.2204, Adjusted R-squared:  0.1424 
## F-statistic: 2.827 on 5 and 50 DF,  p-value: 0.02523
## 
## 
## Summary for RT_MUL3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -13.337  -2.616  -0.448   2.961  12.823 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    20.8135           NA     2.6831   7.757 3.95e-10 ***
## age            -0.4223      -0.3462     0.1607  -2.627   0.0114 *  
## RD_lh_mlf       4.7201       0.7611     3.2538   1.451   0.1531    
## RD_rh_mlf      -6.3761      -1.0281     3.6895  -1.728   0.0901 .  
## age:RD_lh_mlf  -0.1644      -0.4361     0.1934  -0.850   0.3992    
## age:RD_rh_mlf   0.2701       0.7612     0.2097   1.288   0.2038    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.699 on 50 degrees of freedom
## Multiple R-squared:  0.2322, Adjusted R-squared:  0.1554 
## F-statistic: 3.024 on 5 and 50 DF,  p-value: 0.0184
## 
## 
## Summary for RT_DIV1_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.5500 -0.8730 -0.2300  0.4543 10.5142 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    4.38629           NA    0.80329   5.460 1.49e-06 ***
## age           -0.12084     -0.35430    0.04813  -2.511   0.0153 *  
## RD_lh_mlf     -0.59904     -0.34545    0.97415  -0.615   0.5414    
## RD_rh_mlf      0.06441      0.03715    1.10461   0.058   0.9537    
## age:RD_lh_mlf  0.03732      0.35404    0.05790   0.645   0.5221    
## age:RD_rh_mlf -0.01116     -0.11245    0.06279  -0.178   0.8597    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.706 on 50 degrees of freedom
## Multiple R-squared:  0.1198, Adjusted R-squared:  0.03179 
## F-statistic: 1.361 on 5 and 50 DF,  p-value: 0.2548
## 
## 
## Summary for RT_DIV2_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -8.0688 -2.2054 -0.6775  1.6506 11.5302 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   12.728121           NA   1.956580   6.505 3.57e-08 ***
## age           -0.272891    -0.318883   0.117222  -2.328    0.024 *  
## RD_lh_mlf      0.783451     0.180065   2.372761   0.330    0.743    
## RD_rh_mlf      0.496095     0.114020   2.690511   0.184    0.854    
## age:RD_lh_mlf  0.007855     0.029698   0.141020   0.056    0.956    
## age:RD_rh_mlf -0.032492    -0.130531   0.152941  -0.212    0.833    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.156 on 50 degrees of freedom
## Multiple R-squared:  0.1705, Adjusted R-squared:  0.08758 
## F-statistic: 2.056 on 5 and 50 DF,  p-value: 0.08672
## 
## 
## Summary for RT_DIV3_RD_lh_mlf_RD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -14.7807  -3.4483  -0.4494   3.6501  15.9075 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    16.3133           NA     2.5922   6.293 7.65e-08 ***
## age            -0.2445      -0.2141     0.1553  -1.574  0.12175    
## RD_lh_mlf      -9.3441      -1.6098     3.1436  -2.972  0.00453 ** 
## RD_rh_mlf       5.5791       0.9612     3.5646   1.565  0.12385    
## age:RD_lh_mlf   0.4758       1.3484     0.1868   2.547  0.01400 *  
## age:RD_rh_mlf  -0.3024      -0.9105     0.2026  -1.492  0.14193    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.506 on 50 degrees of freedom
## Multiple R-squared:  0.182,  Adjusted R-squared:  0.1002 
## F-statistic: 2.224 on 5 and 50 DF,  p-value: 0.06628
## 
## 
## Summary for ADD1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.183883 -0.016291  0.007712  0.025404  0.052865 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.8961162           NA  0.0195627  45.807   <2e-16 ***
## age            0.0027985    0.3213070  0.0011756   2.380   0.0211 *  
## MD_lh_mlf      0.0399122    0.9013163  0.0238191   1.676   0.1001    
## MD_rh_mlf     -0.0118426   -0.2674360  0.0243370  -0.487   0.6287    
## age:MD_lh_mlf -0.0025048   -0.9203487  0.0014747  -1.699   0.0956 .  
## age:MD_rh_mlf  0.0004261    0.1637404  0.0014591   0.292   0.7715    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04181 on 50 degrees of freedom
## Multiple R-squared:  0.1895, Adjusted R-squared:  0.1085 
## F-statistic: 2.338 on 5 and 50 DF,  p-value: 0.05523
## 
## 
## Summary for ADD2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.33854 -0.03909  0.00807  0.06447  0.18251 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.802791           NA   0.053694  14.951   <2e-16 ***
## age            0.004133     0.181330   0.003227   1.281   0.2062    
## MD_lh_mlf      0.093459     0.806571   0.065377   1.430   0.1591    
## MD_rh_mlf     -0.112999    -0.975198   0.066798  -1.692   0.0969 .  
## age:MD_lh_mlf -0.005631    -0.790699   0.004048  -1.391   0.1703    
## age:MD_rh_mlf  0.005567     0.817513   0.004005   1.390   0.1707    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1148 on 50 degrees of freedom
## Multiple R-squared:  0.1083, Adjusted R-squared:  0.01909 
## F-statistic: 1.214 on 5 and 50 DF,  p-value: 0.3163
## 
## 
## Summary for ADD3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.43572 -0.17334  0.03414  0.16940  0.33702 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.617826           NA   0.094415   6.544 3.11e-08 ***
## age            0.008459     0.209292   0.005674   1.491   0.1423    
## MD_lh_mlf      0.111132     0.540826   0.114957   0.967   0.3383    
## MD_rh_mlf     -0.197026    -0.958832   0.117457  -1.677   0.0997 .  
## age:MD_lh_mlf -0.006023    -0.476912   0.007117  -0.846   0.4014    
## age:MD_rh_mlf  0.009028     0.747671   0.007042   1.282   0.2057    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2018 on 50 degrees of freedom
## Multiple R-squared:  0.1233, Adjusted R-squared:  0.03561 
## F-statistic: 1.406 on 5 and 50 DF,  p-value: 0.2382
## 
## 
## Summary for SUB1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -0.141812 -0.022149  0.007612  0.030978  0.058814 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    9.496e-01           NA  2.115e-02  44.909   <2e-16 ***
## age            6.775e-05    7.749e-03  1.271e-03   0.053    0.958    
## MD_lh_mlf      1.728e-02    3.888e-01  2.575e-02   0.671    0.505    
## MD_rh_mlf     -2.318e-02   -5.214e-01  2.631e-02  -0.881    0.382    
## age:MD_lh_mlf -1.089e-03   -3.986e-01  1.594e-03  -0.683    0.498    
## age:MD_rh_mlf  8.150e-04    3.120e-01  1.577e-03   0.517    0.608    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.04519 on 50 degrees of freedom
## Multiple R-squared:  0.06031,    Adjusted R-squared:  -0.03365 
## F-statistic: 0.6419 on 5 and 50 DF,  p-value: 0.6688
## 
## 
## Summary for SUB2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.46965 -0.03713  0.02813  0.07878  0.18761 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.826093           NA   0.060616  13.628   <2e-16 ***
## age            0.001520     0.057489   0.003643   0.417   0.6783    
## MD_lh_mlf      0.036089     0.268502   0.073804   0.489   0.6270    
## MD_rh_mlf     -0.140031    -1.041841   0.075409  -1.857   0.0692 .  
## age:MD_lh_mlf -0.001168    -0.141353   0.004569  -0.256   0.7994    
## age:MD_rh_mlf  0.005276     0.668026   0.004521   1.167   0.2487    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1296 on 50 degrees of freedom
## Multiple R-squared:  0.1554, Adjusted R-squared:  0.0709 
## F-statistic: 1.839 on 5 and 50 DF,  p-value: 0.1221
## 
## 
## Summary for SUB3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63085 -0.20301  0.04268  0.18095  0.41680 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.697815           NA   0.126360   5.522  1.2e-06 ***
## age           -0.002111    -0.040641   0.007593  -0.278    0.782    
## MD_lh_mlf      0.142601     0.539982   0.153852   0.927    0.358    
## MD_rh_mlf     -0.107457    -0.406905   0.157198  -0.684    0.497    
## age:MD_lh_mlf -0.007479    -0.460822   0.009525  -0.785    0.436    
## age:MD_rh_mlf  0.002888     0.186091   0.009424   0.306    0.761    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2701 on 50 degrees of freedom
## Multiple R-squared:  0.04923,    Adjusted R-squared:  -0.04584 
## F-statistic: 0.5178 on 5 and 50 DF,  p-value: 0.7615
## 
## 
## Summary for MUL1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.16667 -0.02255  0.01112  0.03807  0.05517 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.9157063           NA  0.0236828  38.665   <2e-16 ***
## age            0.0024236    0.2464851  0.0014232   1.703   0.0948 .  
## MD_lh_mlf      0.0043794    0.0876030  0.0288356   0.152   0.8799    
## MD_rh_mlf     -0.0146729   -0.2935065  0.0294626  -0.498   0.6207    
## age:MD_lh_mlf -0.0006445   -0.2097631  0.0017853  -0.361   0.7196    
## age:MD_rh_mlf  0.0014098    0.4799044  0.0017664   0.798   0.4286    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.05062 on 50 degrees of freedom
## Multiple R-squared:  0.06801,    Adjusted R-squared:  -0.02519 
## F-statistic: 0.7297 on 5 and 50 DF,  p-value: 0.6045
## 
## 
## Summary for MUL2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.51142 -0.08140  0.00405  0.13749  0.28081 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.635336           NA   0.086532   7.342 1.75e-09 ***
## age            0.009604     0.249769   0.005200   1.847   0.0707 .  
## MD_lh_mlf      0.101896     0.521193   0.105359   0.967   0.3381    
## MD_rh_mlf     -0.218139    -1.115773   0.107650  -2.026   0.0481 *  
## age:MD_lh_mlf -0.005741    -0.477771   0.006523  -0.880   0.3830    
## age:MD_rh_mlf  0.009875     0.859530   0.006454   1.530   0.1323    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1849 on 50 degrees of freedom
## Multiple R-squared:  0.1865, Adjusted R-squared:  0.1051 
## F-statistic: 2.292 on 5 and 50 DF,  p-value: 0.05948
## 
## 
## Summary for MUL3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -0.5533 -0.1610 -0.0099  0.1759  0.5052 
## 
## Coefficients:
##                 Estimate Standardized Std. Error t value Pr(>|t|)   
## (Intercept)    0.0977152           NA  0.1324755   0.738  0.46420   
## age            0.0267665    0.4423724  0.0079610   3.362  0.00149 **
## MD_lh_mlf      0.0024295    0.0078975  0.1612986   0.015  0.98804   
## MD_rh_mlf      0.0835507    0.2715950  0.1648060   0.507  0.61441   
## age:MD_lh_mlf -0.0052625   -0.2783371  0.0099863  -0.527  0.60054   
## age:MD_rh_mlf -0.0008522   -0.0471402  0.0098806  -0.086  0.93161   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2831 on 50 degrees of freedom
## Multiple R-squared:  0.2299, Adjusted R-squared:  0.1529 
## F-statistic: 2.985 on 5 and 50 DF,  p-value: 0.01959
## 
## 
## Summary for DIV1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.40153 -0.03249  0.02749  0.05767  0.13302 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.850406           NA   0.048028  17.707   <2e-16 ***
## age            0.004497     0.221549   0.002886   1.558   0.1255    
## MD_lh_mlf      0.077886     0.754636   0.058477   1.332   0.1889    
## MD_rh_mlf     -0.114462    -1.109012   0.059749  -1.916   0.0611 .  
## age:MD_lh_mlf -0.004230    -0.666803   0.003620  -1.168   0.2482    
## age:MD_rh_mlf  0.006337     1.044842   0.003582   1.769   0.0830 .  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.1026 on 50 degrees of freedom
## Multiple R-squared:  0.1008, Adjusted R-squared:  0.01084 
## F-statistic: 1.121 on 5 and 50 DF,  p-value: 0.3616
## 
## 
## Summary for DIV2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.55920 -0.13610  0.03164  0.17648  0.34216 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    0.630264           NA   0.106167   5.937 2.75e-07 ***
## age            0.011038     0.230776   0.006380   1.730  0.08978 .  
## MD_lh_mlf      0.196486     0.807977   0.129266   1.520  0.13481    
## MD_rh_mlf     -0.384580    -1.581447   0.132077  -2.912  0.00536 ** 
## age:MD_lh_mlf -0.014375    -0.961778   0.008003  -1.796  0.07851 .  
## age:MD_rh_mlf  0.022449     1.570899   0.007918   2.835  0.00659 ** 
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.2269 on 50 degrees of freedom
## Multiple R-squared:  0.2085, Adjusted R-squared:  0.1293 
## F-statistic: 2.634 on 5 and 50 DF,  p-value: 0.03437
## 
## 
## Summary for DIV3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.63427 -0.23068  0.03154  0.24283  0.45928 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)   
## (Intercept)    0.410785           NA   0.149913   2.740  0.00849 **
## age            0.011375     0.181327   0.009009   1.263  0.21256   
## MD_lh_mlf     -0.062207    -0.195037   0.182530  -0.341  0.73468   
## MD_rh_mlf     -0.004639    -0.014546   0.186499  -0.025  0.98025   
## age:MD_lh_mlf -0.001157    -0.059025   0.011301  -0.102  0.91886   
## age:MD_rh_mlf  0.001883     0.100477   0.011181   0.168  0.86692   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.3204 on 50 degrees of freedom
## Multiple R-squared:  0.08257,    Adjusted R-squared:  -0.009173 
## F-statistic:   0.9 on 5 and 50 DF,  p-value: 0.4885
## 
## 
## Summary for RT_ADD1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -0.80420 -0.36659  0.06126  0.27844  2.40511 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    2.75185           NA    0.25436  10.819 1.07e-14 ***
## age           -0.06534     -0.53579    0.01529  -4.275 8.59e-05 ***
## MD_lh_mlf     -0.22066     -0.35588    0.30970  -0.712    0.479    
## MD_rh_mlf      0.28443      0.45873    0.31644   0.899    0.373    
## age:MD_lh_mlf  0.01280      0.33586    0.01917   0.668    0.508    
## age:MD_rh_mlf -0.01397     -0.38346    0.01897  -0.736    0.465    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.5436 on 50 degrees of freedom
## Multiple R-squared:  0.3011, Adjusted R-squared:  0.2312 
## F-statistic: 4.308 on 5 and 50 DF,  p-value: 0.002456
## 
## 
## Summary for RT_ADD2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -2.7006 -1.1577 -0.0887  0.6728  3.6670 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    7.230173           NA   0.765425   9.446 1.06e-12 ***
## age           -0.151716    -0.436968   0.045997  -3.298   0.0018 ** 
## MD_lh_mlf     -0.254286    -0.144051   0.931961  -0.273   0.7861    
## MD_rh_mlf      0.256597     0.145360   0.952226   0.269   0.7887    
## age:MD_lh_mlf  0.014604     0.134605   0.057699   0.253   0.8012    
## age:MD_rh_mlf -0.004543    -0.043799   0.057089  -0.080   0.9369    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.636 on 50 degrees of freedom
## Multiple R-squared:  0.2192, Adjusted R-squared:  0.1411 
## F-statistic: 2.807 on 5 and 50 DF,  p-value: 0.02603
## 
## 
## Summary for RT_ADD3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.6109 -1.6611 -0.4984  1.1902  8.7478 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   10.80964           NA    1.38156   7.824 3.11e-10 ***
## age           -0.16011     -0.26562    0.08302  -1.929   0.0595 .  
## MD_lh_mlf      1.64055      0.53529    1.68215   0.975   0.3341    
## MD_rh_mlf     -2.02871     -0.66195    1.71873  -1.180   0.2434    
## age:MD_lh_mlf -0.05453     -0.28952    0.10414  -0.524   0.6028    
## age:MD_rh_mlf  0.10725      0.59549    0.10304   1.041   0.3030    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.953 on 50 degrees of freedom
## Multiple R-squared:  0.1561, Adjusted R-squared:  0.07171 
## F-statistic:  1.85 on 5 and 50 DF,  p-value: 0.1202
## 
## 
## Summary for RT_SUB1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.2829 -0.5360 -0.2936  0.3368  9.0256 
## 
## Coefficients:
##                Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.418087           NA   0.666256   5.130 4.73e-06 ***
## age           -0.082496    -0.291637   0.040038  -2.060   0.0446 *  
## MD_lh_mlf     -0.062056    -0.043149   0.811215  -0.076   0.9393    
## MD_rh_mlf      0.528874     0.367737   0.828855   0.638   0.5263    
## age:MD_lh_mlf  0.009264     0.104809   0.050224   0.184   0.8544    
## age:MD_rh_mlf -0.027480    -0.325151   0.049692  -0.553   0.5827    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.424 on 50 degrees of freedom
## Multiple R-squared:  0.1088, Adjusted R-squared:  0.01963 
## F-statistic:  1.22 on 5 and 50 DF,  p-value: 0.3135
## 
## 
## Summary for RT_SUB2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -3.1029 -1.3788 -0.6562  1.2342  9.8200 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    8.16941           NA    1.15183   7.093  4.3e-09 ***
## age           -0.12701     -0.26247    0.06922  -1.835   0.0725 .  
## MD_lh_mlf     -0.19692     -0.08004    1.40243  -0.140   0.8889    
## MD_rh_mlf     -0.62421     -0.25371    1.43293  -0.436   0.6650    
## age:MD_lh_mlf  0.02426      0.16041    0.08683   0.279   0.7811    
## age:MD_rh_mlf  0.03359      0.23230    0.08591   0.391   0.6975    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 2.462 on 50 degrees of freedom
## Multiple R-squared:  0.08981,    Adjusted R-squared:  -0.00121 
## F-statistic: 0.9867 on 5 and 50 DF,  p-value: 0.4353
## 
## 
## Summary for RT_SUB3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -10.8429  -3.2063  -0.9202   2.1233  13.3163 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    17.8007           NA     2.5754   6.912 8.24e-09 ***
## age            -0.3481      -0.3046     0.1548  -2.249   0.0289 *  
## MD_lh_mlf       3.1832       0.5478     3.1357   1.015   0.3149    
## MD_rh_mlf      -6.6287      -1.1408     3.2039  -2.069   0.0437 *  
## age:MD_lh_mlf  -0.1512      -0.4234     0.1941  -0.779   0.4398    
## age:MD_rh_mlf   0.3083       0.9029     0.1921   1.605   0.1148    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.504 on 50 degrees of freedom
## Multiple R-squared:  0.1842, Adjusted R-squared:  0.1026 
## F-statistic: 2.257 on 5 and 50 DF,  p-value: 0.06289
## 
## 
## Summary for RT_MUL1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.3418 -0.5935 -0.1527  0.4242  2.5174 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    3.84690           NA    0.41969   9.166 2.77e-12 ***
## age           -0.10576     -0.52491    0.02522  -4.193 0.000112 ***
## MD_lh_mlf     -0.82295     -0.80334    0.51101  -1.610 0.113594    
## MD_rh_mlf      0.84213      0.82206    0.52212   1.613 0.113058    
## age:MD_lh_mlf  0.04528      0.71914    0.03164   1.431 0.158610    
## age:MD_rh_mlf -0.04318     -0.71729    0.03130  -1.379 0.173892    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 0.897 on 50 degrees of freedom
## Multiple R-squared:  0.303,  Adjusted R-squared:  0.2333 
## F-statistic: 4.346 on 5 and 50 DF,  p-value: 0.002316
## 
## 
## Summary for RT_MUL2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -5.9986 -2.0597 -0.9499  1.2303 11.1527 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   12.15114           NA    1.54474   7.866 2.68e-10 ***
## age           -0.29160     -0.42182    0.09283  -3.141  0.00283 ** 
## MD_lh_mlf     -0.36282     -0.10323    1.88083  -0.193  0.84781    
## MD_rh_mlf     -0.36968     -0.10518    1.92173  -0.192  0.84823    
## age:MD_lh_mlf  0.03297      0.15265    0.11645   0.283  0.77822    
## age:MD_rh_mlf  0.02563      0.12410    0.11521   0.222  0.82485    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 3.302 on 50 degrees of freedom
## Multiple R-squared:  0.1978, Adjusted R-squared:  0.1176 
## F-statistic: 2.465 on 5 and 50 DF,  p-value: 0.04506
## 
## 
## Summary for RT_MUL3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.2024  -3.0038  -0.4117   2.6430  14.0486 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   21.73450           NA    2.65736   8.179  8.8e-11 ***
## age           -0.47394     -0.38855    0.15969  -2.968  0.00459 ** 
## MD_lh_mlf      2.73331      0.44075    3.23553   0.845  0.40226    
## MD_rh_mlf     -6.21328     -1.00190    3.30588  -1.879  0.06602 .  
## age:MD_lh_mlf -0.07772     -0.20390    0.20032  -0.388  0.69969    
## age:MD_rh_mlf  0.25746      0.70648    0.19820   1.299  0.19989    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.68 on 50 degrees of freedom
## Multiple R-squared:  0.2375, Adjusted R-squared:  0.1612 
## F-statistic: 3.115 on 5 and 50 DF,  p-value: 0.01593
## 
## 
## Summary for RT_DIV1_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -1.4827 -0.8712 -0.2528  0.5052 10.4690 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    4.21583           NA    0.79370   5.312 2.51e-06 ***
## age           -0.11362     -0.33314    0.04770  -2.382   0.0211 *  
## MD_lh_mlf     -0.85141     -0.49099    0.96639  -0.881   0.3825    
## MD_rh_mlf      1.02106      0.58882    0.98740   1.034   0.3061    
## age:MD_lh_mlf  0.05015      0.47057    0.05983   0.838   0.4059    
## age:MD_rh_mlf -0.05226     -0.51282    0.05920  -0.883   0.3816    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 1.696 on 50 degrees of freedom
## Multiple R-squared:   0.13,  Adjusted R-squared:  0.04301 
## F-statistic: 1.494 on 5 and 50 DF,  p-value: 0.2085
## 
## 
## Summary for RT_DIV2_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -7.0969 -2.3017 -0.7351  1.4961 12.6145 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)   13.12911           NA    1.97425   6.650 2.12e-08 ***
## age           -0.29518     -0.34492    0.11864  -2.488   0.0162 *  
## MD_lh_mlf     -0.07006     -0.01610    2.40380  -0.029   0.9769    
## MD_rh_mlf      0.27384      0.06294    2.45607   0.111   0.9117    
## age:MD_lh_mlf  0.03863      0.14445    0.14882   0.260   0.7963    
## age:MD_rh_mlf -0.01705     -0.06667    0.14725  -0.116   0.9083    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 4.22 on 50 degrees of freedom
## Multiple R-squared:  0.145,  Adjusted R-squared:  0.05946 
## F-statistic: 1.695 on 5 and 50 DF,  p-value: 0.153
## 
## 
## Summary for RT_DIV3_MD_lh_mlf_MD_rh_mlf__model_standardized :
## 
## Call:
## lm(formula = lm_formula, data = scaled_data)
## 
## Residuals:
##      Min       1Q   Median       3Q      Max 
## -12.9491  -3.4524  -0.2718   3.2149  16.1580 
## 
## Coefficients:
##               Estimate Standardized Std. Error t value Pr(>|t|)    
## (Intercept)    15.5558           NA     2.5675   6.059 1.77e-07 ***
## age            -0.2049      -0.1795     0.1543  -1.328  0.19011    
## MD_lh_mlf      -9.5756      -1.6497     3.1262  -3.063  0.00352 ** 
## MD_rh_mlf       5.6325       0.9704     3.1941   1.763  0.08395 .  
## age:MD_lh_mlf   0.5009       1.4041     0.1935   2.588  0.01260 *  
## age:MD_rh_mlf  -0.2934      -0.8600     0.1915  -1.532  0.13184    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 5.488 on 50 degrees of freedom
## Multiple R-squared:  0.1875, Adjusted R-squared:  0.1062 
## F-statistic: 2.307 on 5 and 50 DF,  p-value: 0.05804

Model statistics

For scaled data

# Define dependent variables
dependent_vars <- c("ADD1", "ADD2", "ADD3", "SUB1", "SUB2", "SUB3", "MUL1", "MUL2", "MUL3", "DIV1", "DIV2", "DIV3",
                    "RT_ADD1", "RT_ADD2", "RT_ADD3", "RT_SUB1", "RT_SUB2", "RT_SUB3", "RT_MUL1", "RT_MUL2",
                    "RT_MUL3", "RT_DIV1", "RT_DIV2", "RT_DIV3")

# List of predictor variable groups
predictor_vars_list <- list(
  c("FA_lh_mlf", "FA_rh_mlf"),
  c("AD_lh_mlf", "AD_rh_mlf"),
  c("RD_lh_mlf", "RD_rh_mlf"),
  c("MD_lh_mlf", "MD_rh_mlf")
)

# Initialize list to store the results
model_stats_list_scaled <- list()

# Outer loop for different sets of predictor variables
for (predictor_vars in predictor_vars_list) {
  # Loop through each dependent variable
  for (dep_var in dependent_vars) {
    lm_formula <- as.formula(paste(dep_var, "~ age * (", paste(predictor_vars, collapse = " + "), ")"))
    lm_results <- lm(lm_formula, data = scaled_data)
    standardized_model <- lm.beta(lm_results)
    model_name <- paste(dep_var, paste(predictor_vars, collapse = "_"), "_model_standardized", sep = "_")
    
    # Collect model statistics
    model_stats <- data.frame(
      Model = model_name,
      R_squared = summary(standardized_model)$r.squared,
      Adjusted_R_squared = summary(standardized_model)$adj.r.squared,
      F_statistic = summary(standardized_model)$fstatistic[1],
      F_p_value = pf(summary(standardized_model)$fstatistic[1], summary(standardized_model)$fstatistic[2], summary(standardized_model)$fstatistic[3], lower.tail = FALSE)
    )
    model_stats_list_scaled[[model_name]] <- model_stats
  }
}

# Combine all model statistics into a single data frame
model_stats_df_scaled <- do.call(rbind, model_stats_list_scaled)

# Write results to CSV
#write.csv(model_stats_df_scaled, "lm_model_statistics_standardized_scaled.csv", row.names = TRUE)
#cat("Model statistics have been exported to lm_model_statistics_standardized_scaled.csv\n")

Age vs DTI scatterplot

#library(scales)
# Define the predictor variables and their new names
predictor_vars <- c("FA_lh_mlf", "FA_rh_mlf", "AD_lh_mlf", "AD_rh_mlf", "RD_lh_mlf", "RD_rh_mlf", "MD_lh_mlf", "MD_rh_mlf")
new_names <- c("FA left MdLF", "FA right MdLF", "AD left MdLF", "AD right MdLF", "RD left MdLF", "RD right MdLF", "MD left MdLF", "MD right MdLF")

# Create a new data frame with formatted values

formatted_data <- data
for (var in predictor_vars) {
  metric <- substr(var, 1, 2)
  
  # Adjust values for MD, RD, and AD
  if (metric %in% c("MD", "RD", "AD")) {
    formatted_data[[var]] <- data[[var]] * 1000
  }
  
  # Round values for FA
  if (metric == "FA") {
    formatted_data[[var]] <- round(data[[var]], digits = 2)
  }
}


# Define colors for each metric
colors <- c("FA" = "#ce6260", "AD" = "#47993d", "RD" = "#59aac2", "MD" = "#eb8a50")
#colors <- c("FA" = "#cc0000", "AD" = "#47993d", "RD" = "#137db7", "MD" = "#f3b72e")

# Create a list to store plots
plots <- list()

# Calculate y-axis limits for each pair of metrics
y_limits <- list()
for (metric in unique(substr(predictor_vars, 1, 2))) {
  relevant_vars <- predictor_vars[substr(predictor_vars, 1, 2) == metric]
  y_min <- min(sapply(relevant_vars, function(var) min(formatted_data[[var]], na.rm = TRUE)))
  y_max <- max(sapply(relevant_vars, function(var) max(formatted_data[[var]], na.rm = TRUE)))
  y_limits[[metric]] <- c(y_min, y_max)
}

# Create scatterplots with regression lines
for (i in seq_along(predictor_vars)) {
  metric <- substr(predictor_vars[i], 1, 2)
  color <- colors[metric]
  
  corr <- cor(formatted_data[[predictor_vars[i]]], formatted_data$age, use = "complete.obs")
  p_value <- cor.test(formatted_data[[predictor_vars[i]]], formatted_data$age)$p.value
  
  p <- ggplot(formatted_data, aes_string(x = "age", y = predictor_vars[i])) +
    geom_point(color = alpha(color, 0.5), size = 2) +  # More transparent dots
    geom_smooth(method = "lm", color = "darkred", size = 0.3, se = FALSE) +  # Dark red and thin regression line
    labs(x = "Age", y = new_names[i]) +
    annotate("text", x = Inf, y = Inf, label = paste0("italic(r) == ", round(corr, 2), " * ',' ~ italic(p) == ", format(p_value, digits = 2, scientific = TRUE)), parse = TRUE, hjust = 1.0, vjust = 3, size = 5) +
    scale_x_continuous(breaks = seq(min(formatted_data$age), max(formatted_data$age), by = 2)) +
    coord_cartesian(ylim = y_limits[[metric]]) + 
    theme_minimal() +
    theme(
        plot.title = element_text(hjust = 0.5),  #  title font size
        axis.title.x = element_text(size = 12),  #  x-axis title font size
        axis.title.y = element_text(size = 12),  #  y-axis title font size
        axis.text.x = element_text(size = 12),  #  x-axis text font size
        axis.text.y = element_text(size = 12),  #  y-axis text font size
        panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1))  # Add thin black axes lines
    #theme(aspect.ratio = 1)
  
  plots[[i]] <- p
}

# Combine all plots into a single figure
scatterplot_age_dti <- wrap_plots(plots, ncol = 2) +
  plot_annotation(title = "Relationships between DTI Metrics and Age") &
  theme(plot.title = element_text(hjust = 0.5, vjust=1, size = 16))

#ggsave("/Users/irina/Downloads/MathDTI/plots/scatterplot_age_dti.png", scatterplot_age_dti, width = 7, height = 8)

# Print the combined plot
print(scatterplot_age_dti)
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Age vs math accuracy: Scatterplot

# Define the predictor variables and their new names
dependent_vars <- c("ADD1", "ADD2", "ADD3", "SUB1", "SUB2", "SUB3", "MUL1", "MUL2", "MUL3", "DIV1", "DIV2", "DIV3")

#"RT_ADD1", "RT_ADD2", "RT_ADD3", "RT_SUB1", "RT_SUB2", "RT_SUB3", "RT_MUL1", "RT_MUL2", "RT_MUL3", "RT_DIV1", "RT_DIV2", "RT_DIV3")
new_names <- c("Addition Level 1", "Addition Level 2", "Addition Level 3", "Subtraction Level 1", "Subtraction Level 2", "Subtraction Level 3", "Multiplication Level 1", "Multiplication Level 2", "Multiplication Level 3", "Division Level 1", "Division Level 2", "Division Level 3")

# Define colors for each metric
colors <- c("ADD" = "#cc0000", "SUB" = "#47993d", "MUL" = "#137db7", "DIV" = "#f3b72e")

# Create a list to store plots
plots <- list()

# Create scatterplots with regression lines
for (i in seq_along(dependent_vars)) {
  metric <- substr(dependent_vars[i], 1, 3) # Extract the first three characters of the string stored in dependent_vars
  color <- colors[metric]
  
  
  corr <- cor(data[[dependent_vars[i]]], data$age, use = "complete.obs")
  p_value <- cor.test(data[[dependent_vars[i]]], data$age)$p.value
  
  p <- ggplot(data, aes_string(x = "age", y = dependent_vars[i])) +
    geom_point(color = alpha(color, 0.7), size = 2) +  
    geom_smooth(method = "lm", color = "darkred", size = 0.3, se = FALSE) +  # Dark red and thin regression line
    labs(x = "Age", y = new_names[i]) +
    annotate("text", x = Inf, y = Inf, label = paste0("italic(r) == ", round(corr, 2), " * ',' ~ italic(p) == ",
    format(p_value, digits = 2, scientific = TRUE)), parse = TRUE, hjust = 1.0, vjust = 3, size = 5) +
    scale_x_continuous(breaks = seq(min(data$age), max(data$age), by = 2)) +
    scale_y_continuous(breaks = seq(0, 1.0, by = 0.2)) +  # Set y-axis limits and step size
    coord_cartesian(ylim = c(0, 1.0)) + 
    theme_minimal() +
    theme(
        plot.title = element_text(hjust = 0.5),  #  title font size
        axis.title.x = element_text(size = 14),  #  x-axis title font size
        axis.title.y = element_text(size = 14),  #  y-axis title font size
        axis.text.x = element_text(size = 12),  #  x-axis text font size
        axis.text.y = element_text(size = 12),  #  y-axis text font size
        panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1))
  
  plots[[i]] <- p
}
# Combine all plots into a single figure
scatterplot_math_age_acc <- wrap_plots(plots, ncol = 3) +
  plot_annotation(title = "Relationships between PMT Accuracy and Age") &
  theme(plot.title = element_text(hjust = 0.5, vjust=1, size = 20))
#ggsave("/Users/irina/Downloads/MathDTI/plots/scatterplot_math_age_acc.png", scatterplot_math_age_acc, width = 9, height = 10)

# Print the combined plot
print(scatterplot_math_age_acc)
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Age vs math RT: Scatterplot

# Define the predictor variables and their new names
dependent_vars <- c("RT_ADD1", "RT_ADD2", "RT_ADD3", "RT_SUB1", "RT_SUB2", "RT_SUB3", "RT_MUL1", "RT_MUL2", "RT_MUL3", "RT_DIV1", "RT_DIV2", "RT_DIV3")

new_names <- c("Addition Level 1", "Addition Level 2", "Addition Level 3", "Subtraction Level 1", "Subtraction Level 2", "Subtraction Level 3", "Multiplication Level 1", "Multiplication Level 2", "Multiplication Level 3", "Division Level 1", "Division Level 2", "Division Level 3")

# Define colors for each metric
#colors <- c("RT_AD" = "#de786a", "RT_SU" = "#00a98f", "RT_MU" = "#456caa", "RT_DI" = "#f3b72e")
colors <- c("RT_AD" = "#cc0000", "RT_SU" = "#47993d", "RT_MU" = "#137db7", "RT_DI" = "#f3b72e")

# Create a list to store plots
plots <- list()

# Create scatterplots with regression lines
for (i in seq_along(dependent_vars)) {
  metric <- substr(dependent_vars[i], 1, 5) # Extract the first three characters of the string stored in dependent_vars
  color <- colors[metric]

  corr <- cor(data[[dependent_vars[i]]], data$age, use = "complete.obs")
  p_value <- cor.test(data[[dependent_vars[i]]], data$age)$p.value
  
  p <- ggplot(data, aes_string(x = "age", y = dependent_vars[i])) +
    geom_point(color = alpha(color, 0.5), size = 2) +  
    geom_smooth(method = "lm", color = "darkred", size = 0.3, se = FALSE) +  # Dark red and thin regression line
    labs(x = "Age", y = new_names[i]) +
    annotate("text", x = Inf, y = Inf, label = paste0("italic(r) == ", round(corr, 2), " * ',' ~ italic(p) == ",
    format(p_value, digits = 2, scientific = FALSE)), parse = TRUE, hjust = 1.0, vjust = 3, size = 5) +
    scale_x_continuous(breaks = seq(min(data$age), max(data$age), by = 2)) +
    scale_y_continuous(breaks = seq(0, 25, by = 5)) +  # Set y-axis limits and step size
    coord_cartesian(ylim = c(0, 20)) + 
    theme_minimal() +
    theme(
        plot.title = element_text(hjust = 0.5),  #  title font size
        axis.title.x = element_text(size = 14),  #  x-axis title font size
        axis.title.y = element_text(size = 14),  #  y-axis title font size
        axis.text.x = element_text(size = 12),  #  x-axis text font size
        axis.text.y = element_text(size = 12),  #  y-axis text font size
        panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1))
  
  plots[[i]] <- p
}

# Combine all plots into a single figure
scatterplot_math_age_rt <- wrap_plots(plots, ncol = 3) +
  plot_annotation(title = "Relationship between PMT Reaction Time and Age") &
  theme(plot.title = element_text(hjust = 0.5, vjust=1, size=20))
#ggsave("/Users/irina/Downloads/MathDTI/plots/scatterplot_math_age_rt.png", scatterplot_math_age_rt, width = 9, height = 10)

# Print the combined plot
print(scatterplot_math_age_rt)
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'
## `geom_smooth()` using formula = 'y ~ x'

Violin plots for accuracy Prepare data

## ACC
# Pivot the dataframe for each operation
data_long_add <- data %>%
  select(age123, ADD1, ADD2, ADD3) %>%
  pivot_longer(cols = starts_with("ADD"), names_to = "Condition", values_to = "Value")

data_long_sub <- data %>%
  select(age123, SUB1, SUB2, SUB3) %>%
  pivot_longer(cols = starts_with("SUB"), names_to = "Condition", values_to = "Value")

data_long_mul <- data %>%
  select(age123, MUL1, MUL2, MUL3) %>%
  pivot_longer(cols = starts_with("MUL"), names_to = "Condition", values_to = "Value")

data_long_div <- data %>%
  select(age123, DIV1, DIV2, DIV3) %>%
  pivot_longer(cols = starts_with("DIV"), names_to = "Condition", values_to = "Value")

# Factorize the age group column for all datasets
data_long_add$age123 <- factor(data_long_add$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_sub$age123 <- factor(data_long_sub$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_mul$age123 <- factor(data_long_mul$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_div$age123 <- factor(data_long_div$age123, labels = c("Children", "Adolescents", "Adults"))

## RT
# Pivot the dataframe for each operation
data_long_add_rt <- data %>%
  select(age123, RT_ADD1, RT_ADD2, RT_ADD3) %>%
  pivot_longer(cols = starts_with("RT_ADD"), names_to = "Condition", values_to = "Value")

data_long_sub_rt <- data %>%
  select(age123, RT_SUB1, RT_SUB2, RT_SUB3) %>%
  pivot_longer(cols = starts_with("RT_SUB"), names_to = "Condition", values_to = "Value")

data_long_mul_rt <- data %>%
  select(age123, RT_MUL1, RT_MUL2, RT_MUL3) %>%
  pivot_longer(cols = starts_with("RT_MUL"), names_to = "Condition", values_to = "Value")

data_long_div_rt <- data %>%
  select(age123, RT_DIV1, RT_DIV2, RT_DIV3) %>%
  pivot_longer(cols = starts_with("RT_DIV"), names_to = "Condition", values_to = "Value")

# Factorize the age group column for all datasets
data_long_add_rt$age123 <- factor(data_long_add_rt$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_sub_rt$age123 <- factor(data_long_sub_rt$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_mul_rt$age123 <- factor(data_long_mul_rt$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_div_rt$age123 <- factor(data_long_div_rt$age123, labels = c("Children", "Adolescents", "Adults"))

Plot ACC

# Create the violin plot for addition
violin_plot_add <- ggplot(data_long_add, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#cc0000", color = "black", alpha = 0.4, width = 1.08, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("ADD1" = "ADD1", "ADD2" = "ADD2", "ADD3" = "ADD3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 1, by = 0.2)) +
  coord_cartesian(ylim = c(-0.3, 1.3)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
       # axis.title.y = element_text(size = rel(2)),
        strip.text = element_text(size = rel(2), vjust = 3, margin = margin(t = 20, b = 5)),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for subtraction
violin_plot_sub <- ggplot(data_long_sub, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#47993d", color = "black", alpha = 0.4, width = 1.08, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("SUB1" = "SUB1", "SUB2" = "SUB2", "SUB3" = "SUB3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 1, by = 0.2)) +
  coord_cartesian(ylim = c(-0.3, 1.3)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
        #axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for multiplication
violin_plot_mul <- ggplot(data_long_mul, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#137db7", color = "black", alpha = 0.4, width = 1.08, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("MUL1" = "MUL1", "MUL2" = "MUL2", "MUL3" = "MUL3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 1, by = 0.2)) +
  coord_cartesian(ylim = c(-0.3, 1.3)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
      #  axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for division
violin_plot_div <- ggplot(data_long_div, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#f3b72e", color = "black", alpha = 0.4, width = 1.08, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("DIV1" = "DIV1", "DIV2" = "DIV2", "DIV3" = "DIV3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 1, by = 0.2)) +
  coord_cartesian(ylim = c(-0.3, 1.3)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
     #   axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create a blank plot with the y-axis label
y_label <- ggplot() + 
  annotate("text", x = 1, y = 1, label = "Accuracy", angle = 90, size = 10) + 
  theme_void() + 
  theme(plot.margin = margin(0, 0, 0, 0))

# Combine the blank plot with the actual plots
violin_acc <- wrap_plots(
  y_label, 
  (violin_plot_add / violin_plot_sub / violin_plot_mul / violin_plot_div) + 
    plot_layout(guides = 'collect'),
  ncol = 2,
  widths = c(0.1, 1)
)

#ggsave("/Users/irina/Downloads/MathDTI/plots/violin_acc.png", violin_acc, width = 12, height = 12)

print(violin_acc)
## Warning: `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.

Plot RT

# Create the violin plot for addition
violin_plot_add_rt <- ggplot(data_long_add_rt, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#cc0000", color = "black", alpha = 0.4, width = 1.4, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("RT_ADD1" = "ADD1", "RT_ADD2" = "ADD2", "RT_ADD3" = "ADD3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 30, by = 5)) +
  coord_cartesian(ylim = c(-3, 30)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
       # axis.title.y = element_text(size = rel(2)),
        strip.text = element_text(size = rel(2), vjust = 3, margin = margin(t = 20, b = 5)),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for subtraction
violin_plot_sub_rt <- ggplot(data_long_sub_rt, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#47993d", color = "black", alpha = 0.4, width = 1.4, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("RT_SUB1" = "SUB1", "RT_SUB2" = "SUB2", "RT_SUB3" = "SUB3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 30, by = 5)) +
  coord_cartesian(ylim = c(-3, 30)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
        #axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for multiplication
violin_plot_mul_rt <- ggplot(data_long_mul_rt, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#137db7", color = "black", alpha = 0.4, width = 1.4, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("RT_MUL1" = "MUL1", "RT_MUL2" = "MUL2", "RT_MUL3" = "MUL3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 40, by = 5)) +
  coord_cartesian(ylim = c(-3, 40)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
      #  axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for division
violin_plot_div_rt <- ggplot(data_long_div_rt, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#f3b72e", color = "black", alpha = 0.4, width = 1.4, size = 0.3) +
  geom_jitter(shape = 16, color = "#000000", size = 0.3, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("RT_DIV1" = "DIV1", "RT_DIV2" = "DIV2", "RT_DIV3" = "DIV3")) +
  scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 40, by = 5)) +
  coord_cartesian(ylim = c(-3, 40)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
        #axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create a blank plot with the y-axis label
y_label <- ggplot() + 
  annotate("text", x = 1, y = 1, label = "Reaction Time", angle = 90, size = 10) + 
  theme_void() + 
  theme(plot.margin = margin(0, 0, 0, 0))

# Combine the blank plot with the actual plots
violin_rt <- wrap_plots(
  y_label, 
  (violin_plot_add_rt / violin_plot_sub_rt / violin_plot_mul_rt / violin_plot_div_rt) + 
    plot_layout(guides = 'collect'),
  ncol = 2,
  widths = c(0.1, 1)
)

#ggsave("/Users/irina/Downloads/MathDTI/plots/violin_rt.png", violin_rt, width = 12, height = 12)

print(violin_rt)
## Warning: `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.

Prepare DTI

## DTI
predictor_vars <- c("FA_lh_mlf", "FA_rh_mlf", "AD_lh_mlf", "AD_rh_mlf", "RD_lh_mlf", "RD_rh_mlf", "MD_lh_mlf", "MD_rh_mlf")

# Create a formatted data frame with adjusted values for MD, RD, and AD
formatted_data <- data
for (var in predictor_vars) {
  metric <- substr(var, 1, 2)
  
  # Adjust values for MD, RD, and AD
  if (metric %in% c("MD", "RD", "AD")) {
    formatted_data[[var]] <- data[[var]] * 1000
  }
}

# Pivot the dataframe for each operation
data_long_fa <- formatted_data %>%
  select(age123, FA_lh_mlf, FA_rh_mlf) %>%
  pivot_longer(cols = starts_with("FA"), names_to = "Condition", values_to = "Value")

data_long_ad <- formatted_data %>%
  select(age123, AD_lh_mlf, AD_rh_mlf) %>%
  pivot_longer(cols = starts_with("AD"), names_to = "Condition", values_to = "Value")

data_long_rd <- formatted_data %>%
  select(age123, RD_lh_mlf, RD_rh_mlf) %>%
  pivot_longer(cols = starts_with("RD"), names_to = "Condition", values_to = "Value")

data_long_md <- formatted_data %>%
  select(age123, MD_lh_mlf, MD_rh_mlf) %>%
  pivot_longer(cols = starts_with("MD"), names_to = "Condition", values_to = "Value")

# Factorize the age group column for all datasets
data_long_fa$age123 <- factor(data_long_fa$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_ad$age123 <- factor(data_long_ad$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_rd$age123 <- factor(data_long_rd$age123, labels = c("Children", "Adolescents", "Adults"))
data_long_md$age123 <- factor(data_long_md$age123, labels = c("Children", "Adolescents", "Adults"))

Plot DTI

# Create the violin plot for addition
violin_plot_fa <- ggplot(data_long_fa, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#b3dcff", color = "black", alpha = 0.3, width = 1.08, size = 0.1) +
  geom_jitter(shape = 16, color = "#000000", size = 0.4, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("FA_lh_mlf" = "FA left", "FA_rh_mlf" = "FA right")) +
  #scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 30, by = 5)) +
  coord_cartesian(ylim = c(0.20, 0.37)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
       # axis.title.y = element_text(size = rel(2)),
        strip.text = element_text(size = rel(2), vjust = 3, margin = margin(t = 20, b = 5)),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for subtraction
violin_plot_ad <- ggplot(data_long_ad, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#7868a2", color = "black", alpha = 0.3, width = 1.08, size = 0.1) +
  geom_jitter(shape = 16, color = "#000000", size = 0.4, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("AD_lh_mlf" = "AD left", "AD_rh_mlf" = "AD right")) +
  #scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 30, by = 5)) +
  coord_cartesian(ylim = c(0.8, 1.2)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
        #axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for multiplication
violin_plot_rd <- ggplot(data_long_rd, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#416753", color = "black", alpha = 0.3, width = 1.08, size = 0.1) +
  geom_jitter(shape = 16, color = "#000000", size = 0.4, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("RD_lh_mlf" = "RD left", "RD_rh_mlf" = "RD right")) +
  #scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 40, by = 5)) +
  coord_cartesian(ylim = c(0.5, 0.75)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
      #  axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

# Create the violin plot for division
violin_plot_md <- ggplot(data_long_md, aes(x = Condition, y = Value, fill = age123)) +
  geom_violin(trim = FALSE, fill = "#a0ac48", color = "black", alpha = 0.3, width = 1.08, size = 0.1) +
  geom_jitter(shape = 16, color = "#000000", size = 0.4, width = 0.1) +
  facet_wrap(~ age123, scales = "free") +
  labs(x = NULL, y = NULL) +
  scale_x_discrete(labels = c("MD_lh_mlf" = "MD left", "MD_rh_mlf" = "MD right")) +
  #scale_y_continuous(expand = expansion(mult = c(0, 0.05)), breaks = seq(0, 40, by = 5)) +
  coord_cartesian(ylim = c(0.7, 0.9)) +
  theme_minimal() +
  theme(panel.grid = element_blank(),
        axis.line = element_line(color = "black", size = 0.1),
        axis.text.x = element_text(angle = 0, hjust = 0.5, size = rel(2)),
        axis.text.y = element_text(size = rel(2)),
        #axis.title.y = element_text(size = rel(2)),
        strip.text = element_blank(),
        panel.spacing = unit(1, "lines"),
        legend.position = "none")

violin_dti <- (violin_plot_fa / violin_plot_ad / violin_plot_rd / violin_plot_md)

#ggsave("/Users/irina/Downloads/MathDTI/plots/violin_dti.png", violin_dti, width = 10, height = 10)

print(violin_dti)
## Warning: `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.
## `position_dodge()` requires non-overlapping x intervals.

cc